It’s no good trying to get Danny to admit that there’s any intrinsic difference between designing something high-culture such as a museum or concert hall, and designing a shopping centre, such as the mega-mall he won in a straight fight with commercial architects at Brunnen in Switzerland. "I told the judges I didn’t want to design it as a shopping centre. I wanted to design it as a civic space for people. They’re not going to want to come here just to shop: they will want to come here because it’s a beautiful place. So that shopping is a result of their being here, rather than the other way round." The resulting mall is indeed a piece of civic design, with the big buildings clustering round a typically angular covered public space and bridging a motorway. Views of the fields and mountains beyond are brought right into the heart of the scheme. It’s the opposite of the usual introverted mall design, where the outside world is pointedly ignored. Libeskind’s architecture is often generated by drawing lines which make connections with other places he finds significant. In this case the other place is not urban. It’s the Swiss countryside.

Apropos of shopping, Libeskind makes an interesting point about his origins. Not about his Jewishness, just about being working class. Most architects aren’t. Most architects come from a relatively affluent middle-class background (Britain's Lord Foster - Norman Foster - is a rare architectural exception of a working-class boy made good). This may possibly lead to that snobby distinction between high and low culture which Libeskind obviously doesn’t feel, despite his precocious musical background. "Architecture has always been done for the people with money, with power. But how do you do architecture which is responsive to the public? That’s what I’m interested in - not style categories, or the networking of power groups. It’s about giving something enlightened back to the public."

There are those who find Libeskind’s buildings - such as his "Spiral" design for the V&A - too strange to stomach. Such unfamiliar shapes, it is argued, ignore their context, stick two fingers up to their surroundings. The funny thing is that - once you see them built - this is not the case. His first two German buildings, in Berlin and Osnabruck, are surprisingly self-effacing. They don’t scream at you. They are not chaotic or anarchic. Libeskind understands context, he just treats it differently. "It’s the same context. You just take it one more step. It’s not just that the building fits into its context and is just a passive, inert bit of matter. A building also has a responsibility to transform the context, give it back something more. Not just taking from its surroundings, but also contributing. Enlivening, transforming."

He's not only bankable, but quotable. The new national Museum of Australia in Canberra, by intellectual pranksters Ashton Raggatt McDougall, is already notorious for including a straight copy of the plan form of the Jewish Museum in a section housing the history of the Australian Aborigines. The Libeskind original has thus become a kind of zigzag logo for oppressed peoples everywhere. It's a form of flattery but Danny is not best pleased.

The most visible manifestation of his work in Britain so far is the Imperial War Museum in Manchester. Cheap, relatively simple, it has a lot to do. "It has to communicate the mission of the Imperial War Museum. Which is that war touched people’s lives, that it’s not just about weapons, and that it’s about the ongoing effect of conflict within the framework of the contemporary city - Salford, Trafford, Manchester. The whole vitality of that northern area which has 20 million people. It’s an incredible urban site. And I think it will change people’s ideas of what it is, where they are, and what it’s about."

While southerners continue to shilly-shally about the Spiral, then, northerners have just got on with building Libeskind. Manchester has trumped London just as surely as Manchester United overcomes Arsenal: it will be years before the Spiral finally materialises, assuming it ever does. Such is Libeskind’s global pulling power now, that previously unseen bands of international pilgrims - the new breed of mobile architecture buffs - are likely to find their way to Trafford just to see what he did to follow up the Jewish Museum in Berlin. It may not quite be a Bilbao Guggenheim - it’s a lot smaller, and its skin is made of metal a lot cheaper than Bilbao’s titanium, for instance - but it has the required landmark quality. Libeskind is hot. Anything he does is news. He obviously relishes this. But what he relishes even more is finally getting a piece of real city built.

"The taxi drivers in Manchester - they point out the peak of the Imperial War Museum," he says. "They know who I am, they know what it is. They navigate by it. So," and he beams the beam of the righteously justified architect, which is even brighter than his habitual smile and this glittering Prussian morning, "It’s a place!".

"Daniel Libeskind: The Space of Encounter" is published by Thames and Hudson.