David Hockney is toweringly the greatest British artist alive today. He was born in Bradford, Yorkshire, on July 9, 1937, but, at the age of nearly 75, is producing paintings at a rate that would exhaust an artist half his age.

This week, an exhibition opens at the Royal Academy in London, entitled David Hockney: A Bigger Picture. Normally, when an artist is in his 70s, an exhibition on this scale would be a retrospective, looking back over a lifetime’s achievement. But most of this show — which contains more than 150 artworks, filling room after vast room — has been done in the past eight years.

As you look around the exhibition, you will notice something apart from the great works of art on the walls. You will see the wonder in the faces of the other people looking at them.

They look transported, for Hockney has done what all great artists aim to do — open our eyes and make us see the world again as if for the first time.

Until the last decade, David Hockney spent much of his time in California, where his most famous works were of swimming pools in Los Angeles.

One of these paintings was called A Bigger Splash — a title that did not just describe this bright, joyful canvas, but seemed to sum up Hockney and the reason for his popularity.

He was one of the emblematic figures of the Sixties: a working-class boy from the North of England, who had thrown off the stuffy restraints of the past and was making his own big splash, not in grimy, class-ridden old Britain, but in the sunny freedom of America.

Openly and happily gay, Hockney did not completely turn his back on home. There was a memorable series of portraits of his parents, and he remembers how, when his mother came to stay with him in LA for the first time in her 60s, she said: ‘It’s strange, all this lovely weather and yet you never see any washing out.’

But the tug of home was always strong. And home had one extraordinary feature, so inspirational for any visual artist, which California lacked: ‘You get spring in California,’ he said, ‘but it’s very slight, so when you come back, the seasons hit you more.’

The sheer variety of colours in the British landscape, the play of light, varying with each passing week, is what has inspired our great artists such as Constable and Turner. And Hockney belongs very firmly in this tradition.

A friend of Hockney’s, at the preview of the exhibition, described a dinner party at the artist’s Yorkshire home one springtime.

It was a very convivial evening, and they stayed up late before heading to bed. But at 4am, Hockney’s bleary-eyed guests heard him calling them to come and look at the dawn. They staggered out in their pyjamas. Hockney bundled them into a car and drove them around, showing them the Yorkshire wolds, the trees and the fields quite literally in a new light.

Hockney studied at Bradford School of Art and remains everlastingly grateful that this was an era before art students were encouraged only to play games with modern art ‘installations’, rather than spending years, as he did, simply drawing.

He draws every day. He never stops. And his facility with charcoal and pencil is staggering. Not since Picasso has there been an artist on this planet with a surer grasp of what he is doing when he draws a line or a draughtsman with better co-ordination between hand and eye.

Visual master: Hockney poses in front of his painting at the exhibition, which will run until April

Some of the most breathtaking exhibits in the Royal Academy are the charcoal drawings of trees and fields. But one of the exciting things about Hockney is that he has always been interested in modern inventions and in the connection between technology and art.

There is some amazing work created by Hockney using an iPad. With a £7.99 app called Brushes downloaded from the Apple iTunes store, he turns the iPad into a sketch pad, ‘drawing’ and ‘painting’ directly onto the screen, using his finger or a stylus.

One of the biggest galleries in the Royal Academy is dominated by this truly astonishing iPad series. The Arrival Of Spring In Woldgate in 2011 consists of huge blow-ups of iPad sketches in bright colours, and a series of oil paintings on the same theme. It is as if you are watching the coming of spring itself.

‘What I began to call Action Week,’ says Hockney, ‘when the cow parsley seems to grow a few feet in about a week, always comes around early May . . . the hawthorn blossom was always there in different amounts. Some years a bush had plenty, the next year not so much.

‘A very exciting time, I thought, especially the hawthorn, of which there’s a lot in Woldgate. If this were Japan at a time like that, there would be thousands of cars driving around to take it all in; here, we’re lucky, we have it to ourselves.’

Will showing these pictures lead to the wreckage of Yorkshire by traffic during the first week of May? No — because the message of the exhibition is loud and clear. ‘It doesn’t have to be Woldgate. Your own garden will change just as much.’

There’s a room in the Royal Academy wholly devoted to hawthorn blossom — drawn in charcoal, painted in oils, sketched on the iPad.

These great frothing bushes of creamy blossom are as visionary as Samuel Palmer’s paintings of the blossom in Kent during the early 19th century. And part of the vision is, of course, a vision of England, which, in spite of all our careless rape of the environment, is still a place of magical beauty. Just look.

Gregory Evans, an old friend and long-term manager of his LA studio, says Hockney is painting his boyhood growing up in Yorkshire — which is obviously true. But he is also showing us our own country, to whose stupendous beauty some of us have become blind.

As well as admiring Hockney as an artist, many of us look to him as to a great British hero, an embodiment of everything that is best about this country — not least its humour, for he is always funny, never pretentious.

When he came home and began to look with new eyes at the Yorkshire landscape, he was also a returning exile looking with less admiration at New Britain. Since his childhood, it has become a bossier, more restrictive, more politically correct sort of place, where the busybodies have seized the controls and interfering is deemed to be a virtue.

Honed talent: Hockney conveys feeling in his moving and expressive Winter Timber (2009)

Whatever your view on smoking, Hockney, a lifetime devotee of tobacco, champions a British man or woman’s right to do what they like with their own lungs and their own money.

Yet he came home to an England where the Lib Dems and the Conservative Party (supposedly champions of a libertarian attitude) did nothing to prevent the outright ban on cigarette smoking on trains, in pubs and clubs.

The smoking issue is a parable of what has happened to this country during the years Hockney lived abroad. We’ve become a nanny state, allowing ourselves to be dictated to.

Hockney travels everywhere by car now, enjoying holidays in Europe, as he listens to talking books or his favourite music blaring out of the speakers (he is very deaf). He is not a Little Englander — no great Briton ever is! But he doesn’t like being bossed about.

He is, of course, a champion of art against pseudery and swindling. He has had some stinging things to say about Damien Hirst’s sheep in formaldehyde.

There is much chicanery and bluffing among the dealers and collectors of Brit Art and most of it is rubbish. Meanwhile, a whole generation of art students has been let down by not being taught to draw — as Hockney was taught.

But understandable as Hockney’s rages against bossiness and pretension might be, it is as a great artist that we celebrate him.

While other artists seem only to be playing games or to be painting the same picture over and over again, Hockney, with exuberant generosity, and magnificent energy, works tirelessly and in new ways to open our eyes to the beauty of the world.

Don’t miss this Royal Academy show. It is so easy to think that the glory of British art is all in the past. But there is a giant in our midst.

David Hockney RA: A Bigger Picture is at the Royal Academy from Jan 21 to April 9, 2012. For tickets, call 0844 209 0051.