Later she held court in a restaurant up the coast designed in the 1930s by Denmark's modernist pioneer and architect-designer hero, Arne Jacobsen. This is a white-modern shrine, a Holy of Holies. After various people had stood up to toast her, Zaha too got to her feet. She was nice to all the right people. Then she looked around her, and lost it. "Whose idea was it that the best fun you can have in Copenhagen is to have dinner in a sanatorium?" she drawled, adding: "I'm off to the toilet."

Zaha, you will have gathered, is not a tactful type. She speaks as she finds, in a rich bourbon-and-Marlboro accent (though she does not drink, and says she has not smoked for four years). Some find this frankness alarming, some enchanting. But if you are one of the world's dozen top architects, and the only woman to enjoy that role - let alone a woman who is Iraqi-born - well, she can say what she likes.

This is not unusual in the rarified world she inhabits. Most of the best, most in-demand international architects behave in an equally high-handed fashion: she's just matching the boys in America's exclusive Pritzker Prize club, shot for shot. What makes her cherishable, however, is that unlike most of them, she always lets the mask slip in public. An off-script thought strikes her, and out it comes. And then she shrugs and smiles in her toothy way, as if to say - oh well, ain't nothing but the truth. Frank Gehry and Norman Foster and Renzo Piano and her old boss and chum Rem Koolhaas do not act quite like this when they are let out. Which makes Zaha, I reckon, a national treasure to set alongside volatile Britartist Tracey Emin. Gawd bless yer, Ma'am!

She's a lot more relaxed than she used to be, doubtless because she's building stuff everywhere. She's happy to gossip about her chances in the forthcoming Stirling Prize against the likes of Foster and the office of the late Enric Miralles, he of the Scottish Parliament building. Her assured BMW factory in Leipzig, which in an act of theatrical bravura brings suspended car shells clanking through the office atrium, is fancied by many. She says she has no expectations, but she stays with the conversation, has a sneaking admiration for Miralles.

The £4.5m Ordrupgaard Museum extension is something of a footnote in the onward march of Zaha. Won in competition at a time when she didn't have so much work on, it is a small, fluid exercise in black concrete and glass which doubles the display space of this bijou rural gallery of French Impressionists on Copenhagen's northern fringes.

Architects cannot help influencing each other: the trick is to stay ahead of the game. So Zaha's jagged, splintery early style, now adopted in diluted form by many others, is conspicuously absent here. The curves and loops of the continuous concrete slab forming floor, walls and roof are a much softer proposition. Moulded concrete, however, is not a technology the Danes are very familiar with, and some of this building - in particular the way the rectilinear steel-framed glazing system is cut to join the double-curving roof slab - looks a little botched. The join is anything but neat. Mention this to Zaha, and she just agrees. Yes, she says. It was a bother getting it built. They did it much better at Leipzig.

This insouciance shows through in other ways. Most architects of art galleries go to absurd, complex lengths to get filtered daylight coming down from above. Zaha just slashes simple gashes in the concrete roof and puts in something opaquely translucent. And where there are particularly sensitive drawings and watercolours to protect, she leaves out the daylighting altogether. It works. What's the problem? In the downstairs gallery - where there's a good Gauguin show - two of her walls lean backwards, so putting the pictures on a slight slant. The curators love what they call this "easel-angle". Zaha shrugs again. Easels? What easels? She just did sloping walls, that's all.

It was a treat to behold, Zaha among the Danes. The Nordic regions embracing Babylon. An unlikely meeting, but they got there before the British. Famously the English Establishment in the form of the Millennium Commission did everything in its power to stop her Cardiff Bay Opera House getting built, and - aided by a local hate campaign - succeeded. Being given the Mind Zone in the Millennium Dome to do was scant compensation. Moe recently she's won an opera house in Guangzhou, China, which must help.

Now a number of British buildings are pending - a Maggie's cancer-care centre in Fife, a transport museum in Glasgow, the headquarters of the Architecture Foundation in London - and most prominently the first of the 2012 Olympic buildings to be allocated, the London Aquatics centre with its rather beautifully undulating roof. Very different from her next, imminent, completion: the Phaeno Science Centre in Wolfsburg, Germany, which is like some prehistoric amphibian lurching across the landscape. In a slightly scary way.

Where is Zaha's architecture heading? She admits to no influences beyond Russian Soviet constructivists such as Melnikov. But at the moment it looks a bit Scandinavian, oddly. Somewhere on the faultline between two great Finnish architects: Alvar Aalto with his wavy ceilings, and Eero Saarinen, a master of organically-shaped moulded concrete buildings in the United States in the 1950s. Oh, and there's a bit of Frank Lloyd Wright starting to creep in now. Who'd have thought it? But that's Zaha: off the wall.

www.zaha-hadid.com the world's her concrete cup-cake.
www.ordrupgaard.dk discover a jewel-casket of French Impressionists.