I'm not back!” Nigel Coates, Professor of Architecture at the Royal College of Art and the designer of the Millennium Dome's infamous Body Zone, spits out the word theatrically. “I didn't go. I just chose to... detach myself for a while.”

Pushing 60, yet disarmingly youthful, Coates is, if not back, then definitely on a roll. A decade after being co-opted, briefly, as the incongruous architectural poster-boy for new Labour, then promptly disappearing, Coates is exhibiting 30 works at Milan's glitzy Furniture Fair, opening tomorrow, which makes him, with the likes of Tom Dixon and Ron Arad, one of Britain's foremost designers.

This quiet metamorphosis from A-list architect to designer has gone unnoticed, as if seen as a sideline from his day job at the RCA. Or perhaps because there's a suspicion of architects-turned-designers, despite plenty of evidence - Pugin, the Eames, le Corbusier - to the contrary. Indeed, Coates has been designing chairs, vases, jewellery - anything - for decades. “I have an Italian idea of architecture and design,” he explains. “They're one and the same thing. You can turn your hand to a building or a chair.”

Coates has an Italian way of doing pretty much everything, including his designs, which certainly don't hide their light under a bushel. “I'm not obsessed by sex,” he protests, in mock outrage. This, I remind him, from the man who proposed a penis across the Thames for the Royal Academy's Living Bridges show 12 years ago. But his work, he admits, “seriously flirts with you”.

His flagship Knightsbridge store for Jigsaw, designed in the late 1980s, remains faintly pornographic, with its stiletto-heel façade, wraparound staircase splayed like a tongue, its banisters floppy ended, and, deeper inside, ribbed columns corseted in fabric and clothes hung on ecstatic, arched metal frames, booted and stilletoed. This is S&M shopping. Even his more demure Geffrye Museum extension in East London has a ceiling tightly laced like a bodice. You might call it surreal, “only that implies I'm doing it to disturb, not to enjoy”.

His furniture follows suit. He famously designed a chair incorporating a wooden penis. But even his “straightest” work, sofas and chairs in the Rollover collection for Varaschin, or for Frag, is plump and bosomy: “bottoms for bottoms”. But, he says, it's not so much about sex as sensuality, that a “space can stroke you, tease you. It's a universal language. But in Britain, it's unbelievably suppressed. Anything vaguely penis or vulva-like and people get offended. But what's more intimate than furniture? A chair touches you. Each time you sit on it, it should give you pleasure.”

His maximalist design can be too rich, but it can be coy and witty. His Crusty table reimagines the florid curlicues of conventional Baroque furniture in computer-generated pixels. His Scubist furniture for Fratelli Boffi pulls apart the wooden frames of their traditional collection and reassembles them with legs upside down, cocked, playing footsie with the sitter.

Coates's fruity style is in vogue again, though it has always had intentions more serious than fashion. This is provocation, not gimmickry. The body, he has written, “is your personal piece of architecture”, the conduit through which we experience the world. So why not stimulate it? All he does, he says, is unleash the fantasy dormant in our environment.

He grew up as a gay teenager in Malvern, the determinedly provincial spa town in Worcestershire. “Life wasn't unhappy, just very limited. When I go back there now I can't believe how conservative it is, how I survived it, but I expect I didn't know any different, even if I knew it wasn't really me. I hated it. I couldn't wait to leave.” His father, an engineer, wanted him to get “a proper job. But he'd take us all on family trips to see cathedrals and castles, which kicked off my interest in architecture, and he was a hobby painter, one of those who copy things in minute detail.”

Not Coates. When he looked at the Malvern Hills looming above the town, “they looked to me like a sleeping giant”. When he paints, he paints not like a photographer but in great swirling impressionistic vortices. He likes, he says, to look at things - a chair or a range of hills - and dream in them something bigger, that speaks to us all. When he teaches, too, “I hope I'm teaching students to be open, to discover themselves, not to do the Malvern thing and bring down the net curtains”.

He made his name in the 1980s, alongside Arad and Dixon as British design's young Turks - “We were always in The Face” - creating a sort of industrial Baroque, inspired perhaps, by a decade in which decline and money, dirt and glamour co-existed. He was architecture's Peter Greenaway or Derek Jarman, imagining a lush fantasy sprouting from London's gutters. He had the Covent Garden warehouse and the renown before such now-illustrious colleagues - Rem Koolhaas, Zaha Hadid, Daniel Libeskind - who also emerged from Bloomsbury's design hothouse, the Architectural Association's design hothouse in the 1970s.

Then “it wasn't cool to build”. What was cool was to imagine on paper a new postmodern architectural language to replace deflated modernism. Some went for po-mo historicism, all stage-set pediments; others went for deconstructivism, strange angles and geometries. Coates's vision - first as Nato (Narrative Architecture Today), then as a “proper” firm, Branson Coates - was harder to define. “For me architecture is about experiencing space, and that experience is multilayered and fractured. I wanted to shift, to layer, use allusions, be nimble.” He called his hallucinatory collage city of real, not Disneyish, experiences “Ecstacity”, and found its physical manifestation when he was invited to Tokyo to design a string of bars, restaurants and clubs in the 1980s: “Here was a city like Ecstacity already. Not neat and tidy. Oh, my God, there's a Rastafarian bar eight floors up next to a fetish bar.”

He was an odd choice to be co-opted by new Labour in the late 1990s - like Oasis or the YBAs, his “cool” was borrowed temporarily to lend Whitehall sheen. On Horse Guards Parade, behind 10 Downing Street, he built the high temple of Cool Britannia: the temporary exhibition space powerhouse::uk, “creative Britain's” travelling showcase. He designed the Body Zone, with its giant, genital-less couple. And he built one of the age's defining icons: the ill-fated National Centre for Popular Music in Sheffield, whose commercial failure, despite its thrillingly odd architecture, became a symbol of new Labour's subsequent disappointments. With his cool clothes and flamboyance, he had more edge than Norman Foster.

“As if I wanted to be part of all that? All that boredom.” He spits the word again. We have been bequeathed, he says, the landscape of new Labour, and it sucks: “So po-faced, so up its own arse. As a memorial for a decade it's pretty crap, isn't it? There was just a moment when I knew I didn't want to spend my life filling in forms, taking fat clients out to lunch, then watching my project die by a thousand budget cuts. My role in life is not to build office blocks.”

He got out, and, despite association with two of new Labour's most notorious failures, with his reputation intact. “I didn't want to play the long-suffering ‘creative' architect. Look at the difficulty Zaha still has in Britain today. I'm in my design period right now and I like it. But that's not to say I'll never build buildings again. I will. But you'll just have to wait.” Coy to the end.

The Salone Internazionale del Mobile is in Milan from tomorrow until Monday

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