Sarah Lucas’s new retrospective at the Whitechapel Gallery in east London looks like a junk shop. But I mean that as a compliment; in fact, I haven’t felt so excited by an exhibition in a long time. After walking past a sculpture of a marrow cast in concrete in the foyer, you enter the main space – a raucous jumble of at least 55 works of art stretching back to 1989.

The gallery has the atmosphere of a bargain-basement emporium where you can pick up all sorts of tat, from scuffed second-hand furniture to old leather boots, chipped buckets, tins of Spam, fluorescent strip lights and even toilets – because these are the raw materials of Lucas’s art.

In her sculpture Bitch (1995), for instance, Lucas turns a wooden table on castors into a woman on all fours by dressing it with a torn cotton T-shirt filled with melons standing in for pendulous breasts, while at the other end a vacuum-packed kipper represents a vagina.

Bitch is typical of Lucas’s art during the Nineties: crude, vulgar, rough-and-ready, confrontational – but also funny and compelling. Knocked together in the manner of Picasso’s sculpture of a bull’s head created from nothing but a bicycle’s handlebars and saddle, it embodies Lucas’s couldn’t-care-less spirit, which animates prosaic materials such as cheap nylon stockings, crispy fried eggs, or old fag butts, transmuting them into art.

As a general rule, Lucas’s sculptures never fawn or seek for our approval – they just exist. They can be prickly and aggressive, like an early work from 1991 consisting of a pair of Dr Martens boots with razor blades protruding from the toes, or one of the many photographic self-portraits in which she adopts a butch, don’t-mess-with-me glare. But this spiky attitude only reinforces the sense that if we don’t like her work, then Lucas couldn’t give a damn. I love that.

After graduating from Goldsmiths College, Lucas participated in Damien Hirst’s warehouse group show Freeze, the launch pad of the Young British Artists (YBA) movement. Before long her principal artistic obsession was obvious: sex.

Two Fried Eggs and a Kebab (1992) turns a tabletop into a set of viciously reductive symbols for a naked woman, with congealed yolks for nipples, and a half-eaten pile of meat in place of genitals. Wit is always a prominent part of Lucas’s work, and, on one level, this sculpture is simply a bawdy visual pun. But it is also deliberately filthy and misogynistic, informed by the feminist literature that Lucas was reading as a young artist, and pointing the finger at the incipient lad culture of the Nineties, when it was OK for men to boast about sexual conquests as though their partners were as throwaway as fast food.

Au Naturel (1994) also lampoons sniggering schoolboy suggestiveness. A lumpy mattress oozing stuffing is half-slumped like a torso against a plinth. On one side of it, a cucumber and two oranges form an absurd phallus. On the other, a couple of melons and a bashed red fire bucket create a female equivalent. Together these objects form a bleak tableau redolent of a squalid one-night stand in a bedsit.

In I might be shy but I’m still a pig (2000), a pair of soiled white knickers and two hams with their trotters still attached become vile surrogates for a woman’s haunches and legs, tossed onto a stained mattress so that the meat appears to be leaking rust-coloured bodily fluids. Somehow those trotters make us imagine painted toenails stuffed into cheap high heels.

The whole thing is disgusting. But it is also powerful, a raw fetish evoking sexual abuse or worse – just like Sex Baby Bed Base (2000), in which lemons poking through a T-shirt on a coat hanger resemble barely pubescent breasts, so that the plucked chicken-genitals below are all the more disturbing. Just as astonishing is Bunny Gets Snookered #1 (1997), in which Lucas stuffs cruddy tan tights with kapok and dresses them up in “sexy” stockings, before clamping them to chairs, where they sit limply, with legs splayed.

I appreciate that descriptions of Lucas’s work can make it sound sleazy, even repellent. But this is how it is in Lucas’s world: despite the visual puns, which have a certain coarse, bantering humour, the sex is rarely enjoyable. More often it is dark and despairing – a contemporary incarnation, if you like, of the abject spirit of Walter Sickert’s Camden Town nudes.

What I love about Lucas is that she creates this effect by channelling the red-top vernacular of the street – indeed, I don’t think I have ever been to a show that feels less detached from the everyday hurly-burly occurring outside the gallery’s front door. This is not to say her art lacks sophistication – many of her sculptures incorporate sly asides about 20th-century predecessors such as Marcel Duchamp or Francis Bacon – just that there is something delightfully defiant and freewheeling about this loud-mouthed exhibition. Lucas tells it like it is.

As a refreshing corollary to this, she does not venerate “art”. Her works are tacked to the wall, dumped on the floor – even when they occupy a plinth they are simply supported by temporary stacks of breeze blocks. Nothing feels stuffy or dull. Everything is fresh, even anarchic. After finishing Bitch, Lucas perfunctorily scrawled its title, date and a signature onto the tabletop using a marker pen. If that isn’t an artist playing it cool, I don’t know what is.

And yet despite the lightness of touch of her sculptures, which were apparently made in the blink of an eye and plonked willy-nilly in the gallery, they also manage to pack a hefty punch – not only formally, in that Lucas knows how to work effectively with compositional elements such as colour, mass and space, but also tonally, in that her art can turn on a sixpence from comedy to despair.

That takes serious talent. The exhibition at the Whitechapel confirms that Lucas is the most important of the YBAs, whose work stands the best chance of still feeling relevant in 100 years.