Tucked down a side alley in Camden Town, north London, bound by a railway track, a busy high street and a former cigarette factory, there is a small row of Victorian brick studios. An address is written in fading white paint on an outer wall. Apart from the odd weed, the concrete passageway is clean and free of dustbins and debris. The noise of children playing, of birdsong, piano practice and the strains of Radio 4 suggest a certain kind of genteel neighbourhood. The only hint of anything unusual is a whiff of oil paint emanating from one black door. This is the hideaway of the man whom many believe to be Britain’s greatest living painter.

‘Hello, hello, come in,’ Frank Auerbach says. He is simultaneously expansive and shy; pleased to see me (we go back years) but also a little irritated by any intrusion into his life. ‘Forgive me, but I resent appointments. I resent having to see anybody apart from my sitters, anybody at all,’ he says bluntly.

The room measures about 25ft square. It has been Auerbach’s home and studio since 1954. There are a few pieces of furniture – a small wooden desk and two wooden chairs; the larger, slightly more comfortable one is for sitters. Circles painted in different colours on the lino ensure that the chair’s legs are returned to their correct place. A work in progress is on an easel. Other canvases are turned to face the wall. The floor is covered with globs of paint, the detritus of Auerbach’s method of painting. On every surface there are brushes, rags, pots of paint, spatulas, old newspapers, well-thumbed monographs and a paint-encrusted trolley. Sketchbooks are arranged neatly in one corner, obscured by a collection of plastic bags. The north-facing window is mired with London dust; a weakening autumn sun casts a faint golden wash over the room. On the back wall there is a functional kitchenette, and on a raised platform a single bed. Tacked to the walls are reproductions of two Rembrandts, a Hogarth, a Picasso, random postcards sent by friends, and three large black-and-white reproductions of Auerbach’s own work.

As a young man Auerbach sold his canvases from pavements for a few guineas; these days his major paintings sell for millions of pounds. His work is collected by museums and dedicated individuals. This month the Rijksmuseum and the Ordovas gallery in London will stage an exhibition called Raw Truth, a conversation between six Auerbach paintings and four by Rembrandt. When the show travels to Amsterdam in December Auerbach will become the first living artist ever to show in the Rijksmuseum’s main collection. A retrospective of his work is planned at Tate Britain in January 2015.

These accolades do not matter much to the 82-year-old Auerbach, whose modus operandi has never altered, and almost certainly never will. As long as the four walls remain strong, he will not move from his studio, nor will he award himself any luxuries. ‘I became solvent so late that it’s too late for me to change,’ he says.

Unlike many artists Auerbach does not collect works of art or mistresses. He barely drinks, never travels and seldom socialises. According to his wife, Julia, he has two haircuts a year, wears his clothes until they disintegrate and is not interested in material possessions. He works seven days and five evenings a week and takes one day off a year. When I suggest that this sounds like a hard life, Auerbach looks genuinely perplexed. ‘No! It’s a fun life. It keeps one on one’s toes. People who turn out pictures and think, “How nice,” and then go to the next picture seem terribly boring to me. You might as well work in a factory. The whole thing is about the struggle and the struggle makes it a fun activity.’

So when he wakes up in the morning does he think, ‘Great, another struggle’?

‘I just think I’ve got to get on with it. Sometimes I feel like what Picasso said. “Man is the only animal that puts himself between the shafts of a cart, the carthorse doesn’t, he has to be led.”’

The map of Auerbach’s world is sparse. His paintings reveal a life pared down to a few significant co-ordinates; there is the studio entrance, glimpses of Mornington Crescent, the house next door, a certain tree and a few faces. He does not accept commissions. His sitters include two relations and a couple of friends. None is paid. They come at the same time, on set days, 52 weeks a year. The longest serving sitter, his wife, has notched up 53 years.

In the past Auerbach went to the odd restaurant, the cinema occasionally and the National Gallery weekly, but even these activities have dwindled. The main change is that he now sees his wife three nights a week – rather than one. It is the life of an ascetic, but one dedicated to work instead of religious or spiritual goals. ‘There have been painters who almost haven’t had a life – Mondrian comes to mind, whose life seemed to be very austere and hermit like,’ he says. ‘On the one hand if one didn’t have a life, there would be nothing to paint, but on the other hand if one gave in entirely to life, one wouldn’t have any energy to paint. There is the conflict. On the whole I think it is a creative one.’

Would he describe himself as an obsessive? He hesitates for a moment and then laughs. ‘I would jolly well hope so.’

Auerbach offers me a choice of coffee, tea, green tea or red wine. I choose green tea and he moves around the studio trying to salvage a cleanish cup. Today he is wearing ‘smart’ clothes – 30-year-old chinos and a blue T-shirt. Does he care about clothes? ‘Not at all. It’s a bit late to think of being the Beau Brummel of Camden Town,’ he says. ‘Julia found me a corduroy suit at an agricultural show and she has reordered four times.’ Auerbach is still handsome. His expression is mostly doleful and intense, but this serious demeanour is punctuated by bursts of infectious laughter, when he becomes almost impish, his eyes closed, shoulders shaking, head thrown back, mouth open revealing child-size teeth.

Our first encounter took place in the late 1980s, when I asked Auerbach to appear in a BBC film I was making about the demystification of art. Then as now I was mesmerised by his work, by his ability to capture the essence of a person or place; how the paint on his canvases never seems to dry and ossify but remains vibrant, fluid, jewel-encrusted, fizzing with energy and mystery. His response was an immediate and robust ‘No’. ‘The thing is, painting is mysterious and I don’t want it demystified,’ he wrote to me. ‘It’s no good presenting artists as approachable blokes who happen to paint, although some may have the coolness or grace to lend themselves to this. If I have ever thought of contacting anybody it is the misfit in the backroom who rejects the general public. I am the beast in the burrow who does not wish to be invaded.’

In spite of the rebuttal, we kept in touch, meeting occasionally with friends we had in common, including the painters Lucian Freud, Mike Andrews and RB Kitaj. To that group of clever, informed artists, Auerbach, younger than the rest, seemed to be the painters’ painter. It was Francis Bacon who rang Marlborough Fine Art to say that there was a brilliant artist, so poor that he lived on potatoes and yogurt, whom they must sign up immediately. Lucian Freud amassed the biggest private collection of Auerbach’s work and used to ask his advice about unfinished paintings. In 1993, when Freud had a major retrospective at the Whitechapel Gallery, I remember Auerbach taking the decisions about where to place pictures, watched by a nervous Freud. ‘He had no sense of hanging a show at all,’ Auerbach says.

Occasionally I witnessed Auerbach and Freud talking about art; there was an air of competitiveness between these two titans of erudition. ‘I do miss Lucian, we were friends for 55 years, or was it 60?’ Auerbach says. ‘He was basically a very nice man and a loyal friend. He was sort of harum-scarum, cutting corners off life, but there was an element of brilliant common sense about his way of looking at things.’ In most respects the two men’s lifestyles were quite different. Although they both worked intensively, Freud loved parties and clubs. ‘Lucian got more into a day than anybody I have ever known,’ Auerbach says. ‘I don’t think he slept more than four hours out of 24. In a way he behaved heroically. Very few people do exactly what they feel like doing. It takes some character.’

Does Auerbach resent being lumped into the so-called School of London along with Freud, Michael Andrews, Leon Kossoff, Francis Bacon and such affiliates as RB Kitaj? ‘I never wanted to belong to a school. The School of London [idea] was total rubbish,’ he says firmly. ‘But I think they are very good painters and I am not ashamed to be put in the same category as them.’ Most have now died. Does he miss them? ‘As time goes on I feel these people are in the room with me.’ Then he stops for a moment, a rare breath in a long, eloquent train of thought. ‘I actually feel sorry for these dead painters who can no longer take part in this marvellously engaging activity.’

In the mid-1990s I started working (coincidentally) with Auerbach’s son, Jake, first at the BBC and then when we set up a film company. In ‘water-cooler’ moments we would exchange family news. Through these stories, another Frank Auerbach emerged. This one liked lewd music-hall songs, Billy Crystal films and southern Indian curry houses.

In 2001 Auerbach finally agreed to let me direct (and Jake produce) a filmed portrait, To the Studio. Wanting to retain the feeling of intimacy and insularity of Auerbach’s life, we decided not to use a film crew. Borrowing a hand-held camera from a friend, we followed the sitters on their journey to the studio, where we filmed Auerbach talking expansively about his life and work.

The longest-serving and most touching sitter is Julia Auerbach. As a beautiful young art student, Julia Wolstenholme fell in love first with one of Auerbach’s drawings, and later with the man. They married and Julia gave birth to Jake in 1958. Unable to cope with domestic life, Auerbach returned to his mistress, Stella West, referred to as EOW in his titles. ‘It occasionally comes to haunt me, the bad behaviour of my youth. I think, how the bloody hell could I possibly have behaved like that?’ Auerbach says of his younger self. ‘But if one didn’t behave badly then perhaps one wouldn’t behave at all.’

Julia raised Jake alone in Sheffield. She and Auerbach got back together in 1976 – now it is hard to imagine them apart. These days she sits (‘He has me lying down mostly’) three times a week. When I made the film in 2001 I asked Julia and the other sitters to describe what the experience was like, week in week out. ‘You are giving yourself up, it’s very intimate, you are vulnerable and you are there for them to do what they want,’ Julia said. Does she feel like his muse? She shook her head. ‘No. I just do it. It sounds a bit awful but it’s like you wash up.’ Stella West, now in her 90s, sat for Auerbach for 23 years from 1948. ‘He used to curse and swear and throw gobbets of paint,’ she said. ‘Sometimes he thought I had dropped off to sleep and he would get angry.’ Why did she put up with it? ‘Because I loved him and he wanted it.’ For Auerbach, being ‘violently impatient with the inadequate in your painting and prepared to do absolutely anything arbitrary in order to kick the painting into a sort of life’ is an essential part of his process.

Jake Auerbach has sat every Tuesday for 37 years. In the beginning, sitting gave him the opportunity to get to know his estranged father. ‘Now I go because I want to, and it’s time well spent, forced to do nothing, away from emails and the telephone,’ he says. Catherine Lampert first sat for Auerbach in 1978. ‘It’s a great pleasure to be able to reflect on things and share it silently,’ she told me. ‘I always come out in a better mood.’ David Landau, who has returned to the studio once a week for nearly 30 years, said, ‘Frank takes so much trouble to convey our lives and our existence it makes us feel that we matter.’ Only ill health stopped Juliet Yardly Mills (JYM) from sitting. ‘I still wake up every Sunday morning at 4.30 and think, “Oh, good, I have got to get ready for Frank,” and then remember that I don’t anymore. That is very sad. I miss it dreadfully,’ she told me in 2001, shortly before her death.

So why does Auerbach paint the same face, the same view over and over again? Wouldn’t it be interesting to try a new landscape or a different nose? Auerbach shakes his head. ‘The closer one is to something, the more likely it is to be beautiful,’ he says. ‘The whole business of painting is very much to do with forgetting oneself and being able to act instinctively. I find myself simply more engaged when I know the people. They get older and change; there is something touching about that, about recording something that’s getting on.’ Amid the frenzy of paint and energy it can be hard to spot the person in an Auerbach portrait. ‘Likeness is a very complicated business indeed,’ he says. ‘If something looks like a painting it does not look like an experience; if something looks like a portrait it doesn’t really look like a person.’

Most artists work on a picture bit by bit, building on composition and detail in each session. Auerbach makes preparatory drawings but always paints the entire canvas anew in a single session. ‘I try to paint the whole picture all the time. Even a beautifully painted section is not of the slightest use to me unless everything is interdependent and lives within the same flow,’ he says. If the composition doesn’t work, then he scrapes off all the paint, again and again, leaving only a ghostly outline on the canvas. ‘If I had 200 blank canvases maybe I would get one right,’ he says. Often a picture takes many hundreds of sessions to finish. The younger Auerbach piled on so many layers of paint that the canvases were too heavy to hang on a wall.

How does he know when a picture is finished?

‘I want everything in the painting to work, that is, every force, every plane, every direction to relate to every other direction in the painting – so there’s no paradiddle or blot somewhere. I feel very strongly that if a painting is going to work, it has to work before you have a chance to read it. Great Rembrandts shake you. There is a tension between unity and difference; one great wave or wind holding it all together as one. A [good] painting concentrates the experience of being.’

A ‘finished’ work goes through a lengthy post-completion process. Auerbach takes the wet canvas and places it in a wooden box. The box is put on top of a high cupboard for two weeks. Then he calls his dealer, Geoffrey Parton at Marlborough Fine Art, who sends a handler to pick it up. The moment Parton receives it he calls Auerbach, and the two men discuss it briefly. Then Parton puts the picture back in the box on top of his filing cabinet for another six weeks. The painting is photographed and the black-and-white reproduction is sent back to the studio. Only then will Auerbach decide if the composition works. ‘One hasn’t committed a sin until one has let out a bad painting,’ he says. Once he told Geoffrey Parton to buy back a work at auction. He completely repainted the image before sending it out on its way again.

I suggest that even great painters have uneven moments. Auerbach agrees, using Rembrandt as an example. ‘The great ones are marvellous, but there are etchings that are overworked and padded. And there are certain paintings which are a bit on the soppy side. But the great paintings are very great paintings. I have never failed to be moved by Rembrandt.’ I wonder if Auerbach feels daunted by the forthcoming show, by the inevitable comparisons between their work? Although there are obvious similarities between the two artists – a tendency to use thick paint, working for long periods with earth colours, painting obsessively – it must be a tall order to match oneself against a great master. ‘Am I worthy of it? I am not the person to judge,’ he says firmly.

Does Auerbach feel competitive with Rembrandt and other artists? ‘When I was young, I felt like I was in the ring with them. Now I just need their help. Recently Delacroix has been present, and Picasso is always there, exhorting me to be naughtier,’ Auerbach says. As a 17-year-old, straight out of boarding school, Auerbach enrolled at Borough Polytechnic, where the Vorticist David Bomberg taught him. Bomberg had been taught by Sickert, who learnt from Degas, who sat at the feet of Ingres. Ingres was taught by David, David by Boucher, Boucher by Watteau, Watteau by Rubens and so on. Does Auerbach feel part of a great family tree of artists? ‘I am a pygmy compared with Michelangelo. Think of the Sistine Chapel, think of the Medici tombs, these are gigantic efforts. Think of Rubens’s work. Of Rembrandt. But painting has its own code of honour; it is our battlefield. Unless you try and do something in the shadow of these great people then it’s all pointless.’

On an easel there is a new work, one of the first of a series of interiors of his studio. Since a double hip replacement last year Auerbach has found it harder to take long early-morning walks to familiar places. He gets up at five and sketches for a few hours, but does not roam far. I ask how age affects his life and work. ‘I always felt time’s winged chariot hurrying near,’ he says quoting Andrew Marvell. ‘I even put that quote into my application to the Slade [more than 60] years ago.’ Surely most young men feel immortal? ‘I suppose my background must have a little bit to do with it. I was uprooted and made aware of the precariousness of things.’

Born on April 29 1931 in Berlin to Jewish parents, Charlotte, a former art student, and Max, a patent lawyer, Auerbach was a child during the rise of the Nazi party. Auerbach remembers ‘a rather bourgeois life’, a nanny and velvet knickerbockers. By 1939 his parents were sufficiently worried by events unfolding in Germany to send their son with the Kindertransport to England. In the film I asked Auerbach if his mother had given him anything to bring on his long journey. At first he said no. Then he suddenly remembered that there was a small suitcase; his mother had had a premonition that they might not meet again. ‘I had some things for wearing immediately and then on some items my mother had stitched a red cross in the corner for later use, and some items like tablecloths and sheets were for use when I was grown up.’

For a time he received letters from his parents via the Red Cross, then they stopped. ‘I don’t remember a specific trauma or upset at being told they had died.’ Many years later Auerbach found out they had been killed at Auschwitz in 1943. Does he dwell on this or on his early childhood? ‘I never look back. I block out everything and just carry on,’ he says. But this same person claims, ‘Absolutely bloody everything feeds into my work. Someone can annoy you; the man at the shop corner does not say good morning. It all feeds in.’

Why, then, does he drive himself so hard? Who or what is the demon on his back? ‘I have always worked from dissatisfaction. I always feel it could have been better, and quite often I feel it could have been different,’ he says. Do you ever give yourself a pat on the back? He looks absolutely appalled. ‘No’.

Auerbach puts his hand over his face and looks at the floor; we sit quietly for a few moments. Then he starts to ruminate on my question. ‘I think it has to do with death. My childhood and biographical reasons – I think I must have felt that unless one justifies one’s life and has something to show for it, then the whole thing is wasted.’

When the afternoon sun dips and the light in the studio fades, I reluctantly say goodbye. Walking back into Camden Town I worry how to capture this man in words. It’s too easy to make Auerbach seem a slightly dotty misanthrope; this is entirely wrong. He is charming, funny, serious, magnanimous and erudite. Speaking in long discursive paragraphs, his conversation skips from Marvell to Yeats, from Rembrandt to Picasso, from Assad to the Plantagenets, via Denis Thatcher’s pink eye. Most unusually and disarmingly he answers questions with candour and honesty. Little wonder his sitters return week after week, year after year. Auerbach’s view of himself is typically self-effacing: ‘Believe me, I am not in any sense unique.’