Architecture: What Zaha Hadid next

The catalogue to a new exhibition opening on 8 October at the Hayward, called Addressing the Century: 100 years of Art & Fashion, shows a little statue by Oskar Schlemmer, head of the Bauhaus school in 1925. With its satellite dish for a head, power-dressed sleeves with studs on, and hula-hoop skirt in steel on tiptoed wire points, it both highlights the fact that fashion can be timeless, and shows what has fallen out of fashion this century: the crossover between art and fashion and architecture. The curator of the exhibition, Peter Wollen, believes that by signing up architect Zaha Hadid to design it, they ended up with more than just a new outfit. They are signalling a trend: the new era of Arts and Crafts, with collaboration between designer-makers, architects and artists. The language of this collaboration and the technology to make it happen is different to that of the Arts and Crafts movement that kick-started the century, but the Utopian ideals behind the movement have come full circle.

Single-minded in the pursuit of perfection, Zaha Hadid explores every option on a site. "I actually like Brutalist architecture a lot. Much more than the glaring minimalist white boxes that pass for galleries these days," she says. "But what it needs is a study, a rethink to devise ways of using the space better."

Her stand at Interbuild for Blueprint magazine, that looked as though a harp had gone through Mach 4, won her the commission from Dr Fiona Bradley of the Hayward. It was an inspired choice. Zaha is passionate about fashion. Her wardrobe is crammed with Issey Miyake and Yohji Yamamoto - "a serious omission in the show" she believes - and designer-label shoes still in their boxes. She famously kept Lord Snowdon waiting for an hour in the airport lounge that doubles as her living- room at home when he came to take her portrait for Vogue. He was like a sidewinder until she sashayed in wearing a big smile, six-inch Manolo stilettos and an Issey Miyake Pleats Please upside down (the sleeves tied around her waist and the waistband framing her face), all of which totally disarmed him. "Wearing Miyake upside down or inside out means that I can double the use, and I don't have to think about what to wear, I just squash it into a suitcase. They're very modern pieces and they don't need the sort of care that antiquities do."

The Hayward, with its grey-suited cement walls and scratchy surfaces, has never looked so good. First, she freed the space of partition walls and unblocked the viewing windows and the stairs to make the space seamless. Then she draped the hunky Hayward in an asymmetrical installation that allows its sinewy grey Brutalist body to show through. Off the catwalk, clothes can fall a bit flat, but her strange catwalks, spiralling ramps and vertiginous tower block bring the garments to life by manipulating the way in which we view them. By altering our focus and tunnelling our vision, she either distances us or draws us closer to the objects under scrutiny. Her installation brings the clothes to life without that age- old solution, dummies, which curator Peter Wollen dismisses as the "herbaceous border of exhibition design". This is all the more remarkable because textiles have to be exhibited under rigorous conditions. No strong light, more shadow and no air conditioning.

Just as dressmakers use paper patterns to make a fashion statement, Zaha Hadid took five garments from the five eras explored in the exhibition - decoration of the turn of the century, function of the Twenties, fantasy of the Thirties, explosion of the Sixties and convergence in the Nineties - as a template. Then she pixillated each one in a computer, and played around with it to come up with an installation "to create a series of fields - a sort of urban landscape - that tells the story of fashion".

In "Decoration" (1900-1920), she flattens the clothes inside low-lying cases that you gaze into, like viewing an archaeological dig. Inside the cases you will find a quilted golden silk mandarin's jacket with pompoms and a matching outsize beret, a costume designed by Matisse in 1920. The inspiration for the shape of the cabinets is a bold black and white fabric design by Raoul Dufy used on a pear-shaped fur-trimmed coat by Paul Poiret, the man who freed women from corsets. But just as Dufy's paisley pattern was more mango-shaped, Hadid's lozenges end up rather like the Cubist pattern on Roger Fry's colourful Harlequin pyjamas, run up by Vanessa Bell at the Omega workshops in 1925. "Flying above, you'd recognise the pattern even though we distorted it," project architect from Hadid's office, Oliver Domeisen insists.

"Function" (1920s) is set amidst a forest of columns inspired by the diagonal slashes Oskar Schlemmer put on a theatrical mask. It could be one of those vertiginous New York cityscapes, with red, blue, silver-grey painted triangular columns that tunnel the vision onto the weird little ballet-dancer sculpture by Oskar Schlemmer, Sonia Delaunay's geometric textiles, and a dress by Madame Vionnet, the architect of couture whose bias-cutting transformed modern dressmaking. The influences of Constructivism and Suprematism are housed in Tatlinesque towers, reminding us that three years ago, Zaha Hadid's installation in the New York Guggenheim for the Russian avant-garde, all sexy curves and risque zigzags, was the talk of the town.

"Fantasy" (1930s) follows "Function" with a series of plinths that tilt on the same rising plane, like a lunar landscape to support the Surrealists. The template was the shadow of a Schiaparelli dress, dissecting the torso into bodyparts, and the effect is as disquieting as Salvador Dal's dinner jacket over a bra supporting hundreds of glass vials filled with creme de menthe exhibited there. At the back, plinths rise to tower overhead while still allowing you to see the contents because of their vertiginous angle.

Forget the Forties and the New Look of Dior. It doesn't interest Peter Wollen because it was a period when art split from fashion: New York became the new art capital of the world while, thanks to Dior's success, Paris remained its fashion capital. Everything was dormant until the Sixties. He calls the jump into the Sixties "Explosion". Perversely, here Zaha Hadid designed a maxi to house the collection of minis. Based on a 1960s Fontana silver dress with peepholes, the display case is stretched across an impossibly long span without any visible support. A column is replaced by suspending it from the ceiling on wires. This is the "shopping arcade" of the Sixties, with Quant and Courreges and Paco Rabanne. Through a periscope you can look into the arcade at hemline level, upon artworks by the likes of LA-based Rudi Gernreich who ruined his reputation early with the monokini, better known as the thong. Like her "maxi", Hadid's latest building takes that same columnless span to an exaggerated 180 metres, at the landscape centre in Basel am Rhein (the same city where Rolf Fehlbaum in the late Eighties commissioned a fire station from her to join buildings by Tadao Ando and Frank Gehry).

"Convergence" is the name of the display of contemporary fashion. The interchange between fashion and art is represented by Martin Margiela, who acid-etched his catwalk collection so that the clothes deconstructed before the show ended, and Helen Storey tells the story of DNA through garments woven with fibre optics. Zaha Hadid designed a catwalk inspired by an Issey Miyake bodice that wraps around the body more like a boomerang than a blouse. When Paul Smith staged his show on this catwalk for London Fashion Week last Saturday, Zaha saw the show as "a sea of fashion editors mostly in black and the models in pastel, an abstract composition not frockland inside the Hayward".

A book, timed to launch with the exhibition, Zaha Hadid - The Complete Buildings and Projects (pounds 16.95, Thames & Hudson) shows that while only a handful of projects over 20 years has been built, she has forged a highly individualistic architectonic language that is at once dynamic and thoughtful.

Her practice, which is run as an experimental studio to develop ideas with a team, has won the commission to design the Cincinatti Contemporary Arts Centre in the States, as well as one of the 11 zones inside the Millennium Dome, the Mind Zone. Only one other practice - Branson Coates for the Body Zone - has been given the go-ahead, which says a lot for the Architectural Association, where both Zaha Hadid and Nigel Coates built fashion and art into architecture.