Rick Mather is the American architect charged with transforming London's South Bank, the world's biggest arts complex. He tells Stephen Moss why he wants to create a mini-city on the Thames

As metaphors go, it's useful. A pile-driver is pummelling a piece of steel into the river beneath Hungerford footbridge on London's South Bank. The noise is so loud that lunchtime joggers cover their ears as they pass, and an elderly couple look on as the metal foundations of a new bridge are slowly sunk. The area had better get used to the pandemonium because, if the plan for the regeneration of the area unveiled yesterday goes ahead, the next decade will be as much about construction as concert-going.

It will, however, all be worth it if the plan, masterminded by the US-born architect Rick Mather, works. The South Bank is a shambles at the moment: walkways that lead nowhere, underground areas that even the drunks seem to think beneath them, gravel car parks, metal fences, brutalist facades. The National Film Theatre is tatty; the Hayward Gallery hard to find; the Queen Elizabeth Hall unloved; the spaces that supposedly connect them a disgrace.

It has been a shambles for a long time and architects have been trying to address the problem for almost 20 years. Terry Farrell spent a decade wrestling with a regeneration plan that was eventually sucked into the mire of political intrigue and planning argument that bedevils the site, the largest arts complex in the world. Richard Rogers's famous "glass wave" roof went the same way, deemed too expensive.

Lessons were learned from the Rogers debacle and the scheme announced yesterday is markedly different from Lord Rogers's bold stroke. Rather than being an architectural démarche, Mather's is a so-called "urban design plan" - an idea for what the place should be rather than how it should look.

Mather has laid down the principles that will be given form by architects following a series of competitions to design the key buildings on the 30-acre site. The South Bank's managers are desperate not to be pinned down to precise figures for the development, because it gives opponents an easy target. The issue of cost is, in any case, clouded by the degree to which the development will be self-financing - there will be a large amount of commercial development, with shops, offices, bars and restaurants.

Mather, the urbane, eternally young 62-year-old who was made "master planner" for the site last year, objects to this obsession with cost. "It's beside the point and confirms the awful generality that Britain is a nation of shopkeepers," he says. Mather was born in Portland, Oregon, but has lived in Britain since the mid-60s and loves London. In fact, he loves cities and his notion is to turn the South Bank into a kind of cultural mini-city.

"Ever since I first came to the South Bank I've imagined what I would do to improve it," he says, "so it was wonderful to get the chance to try. The principles with a city are always the same: you start out with the street and with an active frontage on the street. You have a reasonable density so it's convenient for people walking and you have a variety of different types of accommodation. It has to have balance- between the centre and the ouskirts, activity and peace.

"Streets are precious and wonderful things, particularly ones with lots of people on them, and they should be nurtured and reinforced by the public face that the buildings around them present. All the undercrofts will go and all the street-level car parking too - the things that don't give anything to the street. We're trying to urbanise the site, changing it from a sort of suburban business park into a usable public space.

"But we want to keep some of its character, so it is isn't just like any other urban area. I like the way the precise, pristine Festival Hall is set against the picturesque composition of the 60s buildings. The original designers saw those 60s buildings as a landscape, and they made the analogy with the artificial hill in Regent's Park Zoo that the mountain goats climb up."

Many customers at the South Bank have been less keen than the mountain goats on these 60s brutalist "landscapes", and "picturesque" might not be the word that the layman would apply to the concrete overhangs that dominate the Hayward gallery. So why has Mather decided to preserve it?

"I had to keep an open mind about the 60s buildings," he says. "I had to stay neutral on that or it made a mockery of the whole consultaion process. There's been very extensive consultation on the Hayward and the vast majority of people have been in favour of keeping it. But the 60s buildings can't stay exactly as they are. Functionally they don't work and need modification, and urbanistically they don't work because they don't come down to ground level. They have to change."

Mather is a master of the elegant modification of historically important buildings. He loves glass and that is much in evidence in his visualisation of how the new South Bank might look. "Glass is a good way to fill in under the Hayward," he says. "It makes a nice contrast with the heaviness of the existing building."

One interest group that Mather is not attempting to satisfy are car owners. He is cool, charming and laid-back, except when you ask him where the cars are going to go. "There is this myth that if you want to drive your car, all you need is a parking space," he says. "If you want to drive a car you've got to have a route where you're not stuck in a traffic jam. It's rubbish to say there isn't enough car parking space in the plan. If you have more car parking space, you have longer traffic jams."

He likes to walk and cycle - the best ways to experience the city, he insists - and is a vigorous proponent of public transport. There is a gleam in his eye when he mentions a new scheme for a tunnel linking Embankment tube station with Waterloo.

Now comes the test: raising the money, negotiating the planning hurdles, overseeing the competitions, keeping control of his plan. A good deal will depend on the retailers that move in - the target is very much Borders bookshop rather than Burger King, but isn't there a danger that financial pressures will intrude? "Any good shopping centre is careful about who it lets take space. If you establish the right environment, the right mix, people will be falling over themselves to come here. This might, for example, become the place to sell musical instruments."

Does the Millennium Wheel, which borders the site, help the plan - and will it be a disappointment if it is taken down? "The wheel has been wonderful for the South Bank. Its presence has accelerated the realisation that this is central London, the major space, the place to which the rest of the continent comes. Whether the wheel stays or goes doesn't make a lot of difference to the plan, but it's liked by most people and I notice it has a temporary licence for the same number of years as the Eiffel tower had when it opened."

Don't hold me - or him - to this, but 10 years from now I think we will have a buoyant new cultural mini-city on the South Bank, still towered over by that elegant monument to the millennium.