Soon we are standing in the vast turbine hall of the power station. "Here, you will come in," says Nittve enthusiastically, "and after your 'Wow!' you can find out what is going on in the gallery, and here you will also have your first art experience, hopefully something grand and amazing." This is a great hollow space, 500 feet long and 100 feet high. At the moment, the smell of solvent hangs in the air; dusty shafts of light stream through high windows at either end, and the space hums with the roar and crash of building work. When it's finished it will still be a breathtakingly large hall, and even the most impressive sculptures of the Tate collection will look pretty dwarfed.
Nittve does his best to dispel my feeling that this ocean of space will overwhelm the art inside it. "I, too, was a bit personally worried," he says. "But I have been in discussion with artists about commissioning new work for this area, and they all say 'Fantastic'. We will not necessarily use only huge Richard Serra-type sculpture here, but also projections, or screens, and all sorts of other things. Many different artists have looked at this space. They are very diverse, but they are all very happy to address this space. It is a once-in-a-lifetime thing."
As director of this brand new gallery, opening exactly one year from now, it is Nittve's job to sound upbeat and optimistic. This will be, it is devoutly hoped, the museum that will lay to rest for once and for all any suggestion that the British can't take their art seriously. For the past few decades, the British have looked to the Museum of Modern Art in New York or the Centre Pompidou in Paris and have seen only a symbol of our own inability to keep up. It's interesting that we had to get a Swede in to do the job for us, but we shouldn't hold that against Nittve. He's an enthusiastic, clever man, and although he sometimes sounds more like a walking press release than the art critic he once was - well, how would you talk if you were overseeing a pounds 130m project in a foreign country?
We cross through the turbine room and into the boiler rooms, which will become the gallery spaces. The galleries will take up three of the seven levels here, and most of them will have some natural light pouring in through the sides or from above, thanks to a new glass roof on top of the power station. We struggle through rooms littered with plasterboard and at one point enter a gallery that looks almost finished, a double height room with one high, narrow window running floor to ceiling.
This room is already light and white, like the best galleries. To add to the effect, in the middle of the floor sits a set of steel boxes, while in one corner squats a giant piece of cobalt blue machinery. You wouldn't be surprised if they had tags on them saying Richard Wentworth: Divorce, or Carl Andre: Equivalent IX. "It looks like you've already started moving the exhibits in," I say to Nittve, and he giggles politely. What does he think will inhabit this room when the hanging starts? "The great thing about this room is its height. I would like to use the whole height. I think I would like to show a Joseph Beuys installation here - we have a fantastic one that we're never able to show. It is a cone made of cast mud that comes down from the ceiling."
The last part of the building that we visit is the glass box on the roof. This long, bright room will be a restaurant, and it has the most dazzling views on all sides, including the northern side of the Thames, with St Paul's sitting plumply in the middle of the city. "It's a fabulous location, incredible," says Nittve happily.
It's impossible for me to see exactly how this gallery will work - it's still only a building site inside. But the ambition and scale are certainly impressive. "I have been bringing many artists through to get reactions," says Nittve. "They have been very positive. One of the greatest enthusiasts has been David Hockney. Some people don't find the exterior very exciting, but when they come in they're converted." Back in his office, I see a computer-generated image of the building as it will look when it's finished. The glass roof, which will be lit at night, helps to lift its shape, and the eventual addition of the new pedestrian bridge that will link Bankside to the steps of St Paul's will open it out to the river and make the gallery seem less closed off from its surroundings.
And above all, Nittve wants this gallery to play to its surroundings. "It must feel rooted," he says. "You shouldn't come here and feel that you could be anywhere. You should feel that you are in England, in London, and in a very particular part of London. The key to this is the regular visitors. The community around must feel that it belongs to them." That means that some of the work that the gallery does will take place outside its walls; already it has set up exhibitions and events in the surrounding area, including a performance around a real wedding in Borough market. "We build galleries because artists have been doing art that is fit for museums," says Nittve thoughtfully. "But if artists are working out in society, then we must also follow them."
But the Bankside Tate will primarily be that good old-fashioned thing, a gallery with a large permanent collection. When Nittve took on this job, last September, he had been director of smaller - although highly regarded - museums in Sweden and then in Denmark. One of the great pleasures of this job, he says, has been to discover the strengths of the Tate's collection, most of which is never displayed. "I knew it was a fabulous collection, but I didn't know how good it really was. It doesn't hold to any particular idea of what modern art should be. It doesn't have that view of modern art that it is one linear story.
"But when you look at where art is going now, there are many things in the collection that make it possible to build up a continuum into the present. For instance, there is a wide range of key surrealist works - by Salvador Dali, Max Ernst, and even some women surrealist artists. There are superb Marcel Duchamp works. To have The Large Glass is a major asset. Such things are key to understanding much of what is happening in contemporary art right now."
Sitting in his office, Nittve gets into his stride. "We want to rethink what a gallery of modern art should be in the 21st century. One of the ways to do that is to expand the narrow perspectives that many museums have. That definitely will include gender. It's so obvious that there's been a fairly unconscious but pretty amazing exclusion of women from the dominating art discourse. And we should like to show more from a wider range of countries."
A lot of criticism has recently been directed at the Tate, its director Nicholas Serota, his acquisitions and the Turner Prize for promulgating a narrow vision of contemporary art that privileges conceptual art over all other kinds. When I ask Nittve about it, he is either diplomatic or genuinely supportive of his boss. "For a start," he says, "it's pretty unclear in Britain what's meant by conceptual art. A lot of work that is called conceptual here is in fact pretty retinal - its effect relies on the way it looks, not on the ideas behind it. And I think one can say that what has happened in the past 10 years at the Tate under Nick Serota has made it one of the two or three major museums of modern art in the world. That's not my evaluation - that is an objective fact."
And does Nittve feel that the much hyped renaissance in British art has been a real phenomenon or a storm in a fur-lined teacup? "I think it's fantastic," he says stoutly. "Of course this Brit Art Movement, or the Young British Artists, was really an artificial label. There was this group of strong artists, but they were not that similar. And I think the scene has got even stronger, livelier and more energetic now this package is going away."
Nittve is sure that the British are now more than ready to throw off their traditional unease with visual art. "During most of the modern period, London was a bit on the periphery. There were many creative individuals, but most of the major movements developed in France, Germany, America. This has changed only in the past one or two decades. What made a difference was that wave of great British sculptors, like Woodrow and Kapoor and Cragg. With this gallery, at last we can really show British artists in depth. It will be an eye-opener for visitors. And of course British people are ready for this. After all, the attendance figures for the Tate Gallery at Millbank have more than doubled in the past 10 years. There are so many signs that the position of visual art in Britain has changed tremendously."