Simon Hattenstone talks to Zaha Hadid

You can't miss Zaha Hadid's gold bag. It sits, proud and plump, in the middle of her desk, which sits slap bang in the middle of her London office. The bag is curiously human, smooth and voluptuous as a Henry Moore. The office is an old school classroom, and it looks as school-like as ever. The young pretty boy and girl architects sit in rows, silently fiddling with mice at their computers. I expect to see a cane hanging from the wall.

Gayle, who is head of the press office, tells me that Hadid is on her way. I don't think there is actually a press office as such, but it's very Zaha to call Gayle head of press. Gayle provides a guided tour of the office. Beautiful abstract paintings hang on the wall, part Mondrian, part Miró. It turns out that they have been painted by Hadid, as part of the presentation package for projects.

Gayle puts the video recorder on and sits me in front of the video which shows short films of Hadid's work in progress. They look magnificent. The Rosenthal Centre for Contemporary Arts in Cincinnati is made up of transparent building blocks that slide into each other like a kids' game; the Centre of Contemporary Arts in Rome winds in and out of the landscape like a Scalextric set. She shows me a daunting catalogue of Hadid's work (huge portrait of her on the front - unusual for an architect), with illustrations of her finished buildings - the Vitra fire station in Weil am Rhein, Germany, with its great concrete shard, trying to soar like a one-winged bird; the ehibition hall, also in Weil am Rhein, with its narrow concrete approach that gradually widens until it has turned into the roof of the exhibition centre. The buildings are as magical as they are unlikely.

By the mid-90s Hadid had established herself as 1) the world's greatest woman architect and 2) the visionary who never got her buildings built. She won competition after competition, but the plans and drawings and paintings remained just that. Her nadir came in 1995 when Cardif rejected her futuristic opera house in favour of a new rugby stadium. Now, thankfully, her genius is finally being realised across the world. Except for Britain, of course.

Hadid walks in as I'm watching the videos. She asks if I'm ready for her. Yes, I say. So she trots off. She is having an intense one-way conversation with one of her boys. His bottom lip seems to be quivering. A few minutes later she returns and ask me if I'm ready for her yet. Yes, I say. And off she trots again, to talk to another office junior.

Eventually, she returns. She is dressed, as usual, in black - leggings, top, kittenish boots and a jacket (she always wears Issey Miyake) that gives her wings when she spreads her arms. Hadid's lapis lazuli ring, shaped liked a prefect's badge, straddles four fingers. Her lips are glossed pink, her head hennaed, red-orange-brown. Somehow Hadid, 52, carries it off.

It must be amazing, I say, to finally see your dreams being realised. "I know," she says, grinning as she shows me more models of buildings under construction. Hadid was barely 30 - a baby in architect terms - when she won her first competition. So why did she have to wait 20 years to put theory into practice? "Well, I think there are two reasons. The primary reason is because people were not used to them. Second, there is an element of prejudice and an element of resistance." She seems pleased with her understatement.

In fact, architecture may well be the last bastion of sexism. I tell her I don't know of any other famous women architects. She nods. Why not? "It's a combination of things. Achhhuh." She clears her throat. "Architecture is unnecessarily difficult. It's very tough," She talks about the number of hurdles - from conception to planning permission to getting the damned thing built.

Fine, but there are plenty of tough, able women around who can cope with the demands. Oh yes, she says, some of the best students she has worked with have been women, but somehow it still rarely works out. "The problem is that the professional relationship between men and women has never been normalised, so men don't know how to behave with women," she says in that deep rasping Zsa Zsa Gabor voice. At so many boardroom meetings, she says men refuse to address her directly, looking through the window as they talk to her.

"Listen," she says, suddenly whispering. "This is my office and when I tell them something they resist me because I'm a woman. If I tell them that, they would say that's baloney and bull, but there is a resistance." Come on, I say, surely they don't defy you? Her PA, polite as you like, pops into the office with coffee, and a sugar bowl that looks like St Paul's cathedral.

He leaves, and Hadid continues. "You can see if just one of the women does better than them it affects men. I'm not sure in every profession it does, but in architecture it does. I know if I was not bloody-minded, and I really thought it was worth sticking my neck out and keeping on, there were many moments when I could have just given up... because people treat you badly."

She admits she is still devastated by what happened in Cardiff. "Some of them behaved abominably. I should tell you the comments they made. If it was in any other country it would be seen as blasphemy." Go on then? "Well, I mean, they said 'Why should we give this building to a foreigner?' y'know." They actually said that? "Well they didn't actually say it in print but, I mean, Rhodri Morgan said this looks like the Kabbah in Mecca, and that if we built it like that we'd have a Salman Rushdie situation. I mean, how ridiculous is that? And he is a politician."

Hadid was born and grew up in Iraq. Her father was a socialist politician turned industrialist. She grew up as a secular Muslim, attending convent school. In the Iraq of her childhood, women worked and Muslims lived alongside Jews and Christians. She says she felt she could have done anything or become anyone - academic, artist, mathematician.

She has not been back to Iraq for 20 years, and says that she doesn't really want to talk about politics but she is opposed to the war option. "I don't think Bush sorts out problems. There are lots of very smart people in the Middle East, and I think they should bring them together to see what they can do." Who does she regard as a greater threat to world peace, Saddam or Bush? "No comment." Silence. "Being Iraqi taught me to be very cautious." Presumably this is a diplomatic no comment as much as a political one - the arts centre in Cincinnati opens in May.

In her mid teens, she went off to school in Switzerland, studied maths in Beirut and came to Britain to study architecture in 1971. Apart from the temporary Mind Zone at the doomed Millennium Dome, she has still only had one building made in Britain - a tiny one, at that, the £400,000 Maggie Cancer Care Centre in Scotland. "I have no other project here, and I find that sad - for me. And baffling." And she does sound truly baffled.

Does this say more about her or Britain? "More about Britain." As soon as the opera house fiasco happened, she realised that Britain couldn't cope with her imagination. Hadid's work has been called "ecstatic architecture" - a great label. Her buildings tend to be flat, with great big warm spaces inside - the opposite of the phallocentric architecture that dominated the 20th century. Her work is celebratory, playful, and literally breaks down barriers - interiors merge into exteriors, floors turn into walls which turn into ceilings, concrete turns into glass and steel, the transparent turns into the opaque, and impossible angles shoot out of nowhere.

You can't beat a good angle can you, I say. She nods, and licks her pink lips. "There are 360 degrees, so why stick to one?" I ask Hadid what architecture means to her. "It is fundamentally about shelter. At the same time, it should give you pleasure. When people go out on to the fields they are always amazed because of the flatness or the light falling on different mountains, and you can achieve that through architecture. You can create all these incredible spaces with not much difficulty. That's what we're there for. Inventors of space." Buildings, she says, should keep you dry and feed the soul. She picks up a bottle plonked on her desk to explain how architecture has changed through time. "You cannot break this bottle. There is no other bottle. That's what they used to think, and that's changed. And if I contribute to that, great."

Hadid is often referred to as a diva - the stories are legion of her marching into the hairdressers and demanding that she be serviced instantly, being chauffeur-driven round town in her privately-owned black cab, telling powerbrokers where to stick it. Does she think her reputation is deserved? "No. What is a diva? If I was a guy would they call me a diva? I mean, they wouldn't."

Is she as tough as people say? "I don't think I am that tough, actually. Well, tough in the sense that I don't take any rubbish, and that doesn't make me very popular, frankly. I mean, because some people say something to me, and I just tell them off. I mean, why should I put up with it? Or people I don't like, I show them I don't like them. Why should I pretend? Some people put up with being humiliated because they think this person is important to them while some people are just blatantly nasty or hideous, and I don't play up to them, and that hasn't helped me at all. I've always spoken my mind and people don't like it - and I've paid a price for it. People think I'm difficult and therefore they don't give me a project. I've never heard men referred to as difficult."

Does she ever wish she'd kept her mouth shut? She laughs loud and hard, showing off her gap tooth. "I'm much more careful now." Whenever she's telling somebody where to go, she says she tries to leaven it with humour.

She tells me that tomorrow she's off to Athens, back for the weekend, then off to the US next week. That's another reason why so many women find it tough, she says - architecture is not really a profession, it's a life.

Hadid lives by herself in Kensington. I ask her if she has had to make sacrifices to get so far? "No," she says. "No, I haven't. I promise you I think if I had wanted to have children I would have done so. Frankly, there was no time to think about it when I was working." Because she was so driven? "Yeah, and that's why I've never really felt I've sacrificed it. I do think some women think about it differently." Whose shoulder does she cry on when she's stressed? She says she has very good friends.

She talks about how much she loves it when she gets back to London. I tell her it's amazing that she's still here considering the way Britain treats her. "I know. But I like it here." She says it's probably the only place where she can work quietly, anonymously. "If I was in New York they'd be bothering me every minute, but here there is complete privacy." I suggest that she is staying out of pigheadedness; until we learn to appreciate her. She laughs.

Hadid races off back to work, promising me that Gayle will show me round. I ask her if she has a role model. "No, when I was younger I was not one of these people who had heroes. It was difficult to find a hero for myself." Perhaps you are your own role model, I say. "Well, you try," she says.