Designs on an icon

John Pawson is worrying about his white walls. The famously fastidious architect is showing me the plans for his latest project, an £80m scheme to move the Design Museum from its current home in Shad Thames to the remodelled Commonwealth Institute building on Kensington High Street, and the thought of the predicted 500,000 visitors a year running their grubby hands over his pristine creation causes him to pause.

'There will have to be some wood panelling because I want to avoid having white walls where people are going to touch them,' he says. This moment of anxiety is soon over, however, and Pawson returns to looking boyishly excited by what will be his first real public building in Britain. At 62, his reputation rests on a handful of exquisite homes designed in an uncompromising minimalist style for elite clients such as Doris Saatchi, and the private nature of these projects means they are known to just a privileged few. 'One of the great ironies of my architecture is that most people only see it in photographs,' Pawson laments. 'It's very nice for me finally to do a building that you can actually visit.'

The new Design Museum certainly promises to live up to expectations. The former Commonwealth Institute is a heroic Modernist building completed in 1962 and distinguished by its soaring green roof, the mind-bogglingly complex shape of which is officially described as a hyperbolic paraboloid. Pawson's proposals, unveiled last week, show the remodelled interior as a series of elegant gallery spaces around a central atrium over which this breathtaking concoction hovers like a giant bird. There will be a café and restaurant overlooking Holland Park, a shop and a library - all in the prescribed Pawson palette of clean lines, fine finishes and absolutely zero clutter.

While the prospect of enjoying this new public space for its own sake is tantalising (when it opens in 2014, access to much of the building will be free. 'You can just pop in and use the loo if you want to,' says Pawson irreverently), the museum's primary purpose is, of course, to communicate the history and value of contemporary design in all its forms. The permanent collection, in store for the past five years and containing iconic items from Eames chairs to spacesuits, will be housed on the top-floor gallery, while a programme of changing exhibitions will be installed on the lower floors. As a centre for design education and information, the project is the culmination of a life's work for the museum's founder, Sir Terence Conran, who recently turned 80, and the start of a new era for its director, Deyan Sudjic.

As Conran tells it in his rich, cigar-mellowed voice, the history of the Design Museum began in the early 1980s. He had just gone public with his Habitat chain of shops. 'I found myself with quite a pile of money, so I gave 25 per cent of it to the Conran Foundation with the idea that it would promote design.' Conran persuaded Sir Roy Strong, then director of the V&A, that he should provide a space where contemporary design could be shown. This gave birth to the Boilerhouse Project, a gallery within the V&A where the edgy programme was devised by the youthful Stephen Bayley. 'Stephen staged 25 exhibitions in five years, which demonstrated the opportunity for a proper design museum,' recalls Conran. When the Boilerhouse crew was effectively evicted after a gang of V&A curators staged an uprising against what they saw as its overt populism (a show called Coca-Cola - the Making of a Brand was the final straw), Conran came to the rescue. He created a home in a remodelled banana warehouse at his Butler's Wharf development, appointed Bayley as director, and became the founder of Britain's first official Design Museum when it opened in 1989.

Over the next 15 years the museum, a charity that gets only 10 per cent of its funding from the public purse, fought hard to define its role, a battle which at times it badly seemed to be losing. Several directors left under a cloud, and rumours of internal rows over the validity of some shows regularly filtered through the London design community (a 2004 exhibition devoted to the flower arranger Constance Spry apparently caused particular friction between the board and the then director). Despite these hiccups, the Design Museum's best shows have won it a reputation for being smart and significant, and it is this reputation that Deyan Sudjic has quietly consolidated since he was appointed director in 2006.

Sudjic, 59, is in many ways the man the museum has been waiting for. Born to Yugoslavian parents in London 'a five-minute walk from the Commonwealth Institute', he trained as an architect in Edinburgh and worked as a young critic on The Sunday Times before setting up Blueprint, Britain's first magazine of architecture and design, in 1983. During his 12 years as editor, Sudjic travelled the globe interviewing stars in the field and establishing a contacts book that makes his influence in the design world second to none. He also curated exhibitions, wrote books, and worked as architecture critic for The Guardian and the Observer. Later he spent four years as director of Glasgow's widely admired stint as the UK's City of Architecture and Design, a job that he says prepared him well for the challenges he now faces at the museum.

Not surprisingly, Sudjic crossed paths early on with both Conran and Pawson, the former when he became an investor in Blueprint, the latter when he went to interview him. 'Deyan is so sharp and clever,' says Pawson. 'He's very much on a mission - he can see the big picture and he can see the end goal.' In his private life Sudjic is also well connected: his wife Sarah Miller is the editor of Condé Nast Traveller, and her father John Miller is a highly regarded architect who works in practice with his wife Su, the first wife of Richard Rogers and one of the originators of the high-tech movement.

Throughout his time at Blueprint and beyond, Sudjic has never swayed from his belief in the value of good design and architecture to industry, but also as something beautiful and pleasurable that everybody is entitled to enjoy. 'I've always had this sense that the subject is too important and interesting to leave to the priesthood in the professional ghetto,' he says. 'When I was writing I wanted to reach a wider audience; a museum is exactly how you can do that. As print becomes more challenged, I think the museum is a format that will flourish and survive because it's a shared experience.' He points to the 70,000 ticket sales for the Design Museum's 2007 exhibition on the work of architect Zaha Hadid as evidence that there is a public appetite for the subject as well as for the way in which his institution presents it.

With the current Design Museum 'bursting at the seams', as Conran puts it, Sudjic had been on the lookout for a new location. After several friendly but unfruitful discussions about creating a home at Tate Modern or the V&A, the answer came in the form of an unexpected offer. The borough of Kensington and Chelsea wanted a cultural organisation to take over the Commonwealth Institute in order to create a mixed use for a scheme that will also see three blocks of luxury apartments go up around the site. The architect for the apartments is OMA, the practice of the visionary Dutch architect Rem Koolhaas, and the developer, Chelsfield, was willing to give the Grade II*-listed building to the Design Museum in exchange for its commitment to make its new home there. The offer was too good to refuse, especially since Chelsfield added a £20m gift towards the cost of preserving the shell of the building, the payoff for which is that they will have a cool cultural institution at the heart of their swanky development, and one that keeps the planners happy too. Altogether Chelsfield's donation represents nearly half of the capital cost of the project, while more than 60 per cent of the remaining £44.66m needed has already been raised, with £17m coming from Conran in the form of a donation by his Foundation.

After the deal had been agreed, Sudjic set about looking for an architect who could turn the historic but tatty building into a state-of-the-art museum. A competition was held and Pawson selected. What made him stand out? 'When you've got a vigorous building and when your exhibitions are the star of the show, you don't want another architectural voice intruding on that,' explains Sudjic. 'John's work has always been about quietly making something special out of what is already there.' An essential part of the architectural experience for the visitor will be the jaw-dropping impact of the roof - what Sudjic calls 'a sensational moment of wowness' - and Pawson's respectful approach will only enhance that.

As for Terence Conran, he is content that the now safely established museum will be his legacy. 'I used to say Habitat was my greatest achievement,' he says. 'But this is top of the tree.' How far, I wonder, does his role as founder and a trustee involve him in its day-to-day running? 'I don't view it as my museum,' he says. 'But I do voice my opinion.' On one memorable occasion, remembers Sudjic, this manifested itself in a note from Terence on the delicate matter of the acquisition of a Kalashnikov. 'No ornaments!' it read. 'What I actually meant to write of course was no armaments,' laughs Conran.