I first remember encountering Richard Rogers as I was coming out of Voyage, a shop which specialised in extraordinarily expensive, but beautifully made, clothes, run by Italians called Tiziano and Louise Mazilli, in the Fulham Road. I recall someone slightly larger than life, exuding an open, supremely confident, continental prosperity and exoticism, as if London could, after all, be turned into a branch of the Italian Riviera, with hot coloured shirts for sale and coffee shops on every street corner. Since then, I have run into him on several occasions, always suntanned, generous-hearted.

About a year ago, the president of the Royal Academy and I had lunch at the River Café, to consider the idea of allowing him to stage an exhibition in celebration of his 80th birthday in the building we own in Burlington Gardens. It has been an ideal way to bring life to the old mid-Victorian, classical building which, from 1970 to 1997, was The Museum of Mankind, an outpost of the British Museum, staging exhibitions on subjects such as the Mexican Day of the Dead.

Rogers has brought some of his dash and colour and ad hoc innovation to the building, which has been lying underused and seeking a new identity for nearly a century, ever since the University of London moved its headquarters to South Kensington in 1900.

We decided that the exhibition should be lightweight, exploratory and not too celebratory. It was put up at speed, designed by his son Ab, and sharing some of the aesthetic which led to the design of the Centre Pompidou, as different in style from the sort of exhibitions which the Royal Academy normally shows in The Sackler Galleries as the Centre Pompidou was from the Louvre.

He has somehow made work fun; this, too is a great talent.

The format of the exhibition, cram full of material – books, sketches, objects, films and models – allows for an appraisal (or reappraisal) of the key elements of Rogers’ career.

The first thing that is worth saying is that, although in retrospect Rogers’ path looks smooth from being a student at the Architectural Association to postgraduate studies at Yale, where he was taught by Paul Rudolph and the charismatic architectural historian, Vincent Scully, to a partnership with Norman Foster in Team 4, to winning the international competition for the Centre Pompidou with Renzo Piano, who at the time was a partner in his firm, his passage to architectural stardom was, in reality, much less straightforward.

Unsuccessful at school, owing to his dyslexia, he has never been much of an architectural draughtsman and had to be helped in many of his drawings (as well as his typing) by his girlfriends, first Georgie Cheeseman and then Su Brumwell, who he married before going to America, and later by Norman Foster, who has always been much better able to express architectural ideas through drawing.

After three years at the Architectural Association, his tutor, Michael Pattrick, wrote: “The real issue is this: you have some ability in design but, although you are now 24, you seem to be completely incapable of organising your time or acquiring any understanding of the practical side of an architect’s work.”

At the time that he won the competition for the Centre Pompidou, Rogers was aged 36. He had a small number of domestic projects to his name, including Creek Vean in Cornwall for his parents-in-law, a brilliant, modernist house which was based on the houses he had seen in California, and Skybreak House in Radlett, Hertfordshire, which he did for Tony Jaffé.

Both were commissions while he was a member of Team 4. A house in Wimbledon for his parents (currently on the market for £3.2 million), and a house and studio for Humphrey Spender in Ulting, Essex, were done after he had set up in independent practice with his wife, Su.

None of them had been completely straightforward. He had split from Norman Foster. They were two ideologically strong architectural personalities, who had proved incompatible. He had split from wife, Su, who was his partner in his office, and was living with a hippy-ish, young American design student, Ruth Elias.

His practice had no work, other than a politically complicated redevelopment of the Kite area in Cambridge, which he was doing jointly with Leslie Martin and was earning him the enmity of young Cambridge dons. So, while winning the international competition for the Centre Pompidou now looks somehow inevitable, at the time it must have felt like an accident of fate, the work of two unknown architects picked out from 681 entries.

So, what then has led to Rogers’ extraordinary success as an architect? Some of it must be owing to his extraordinary, larger-than-life, sunny personality. There is a photograph of him standing next to Norman Foster on a street in Yale, before embarking on a tour of the works of Frank Lloyd Wright, together with Carl Abbott, the third member of the party.

Foster is wearing a relatively conventional tweed coat, turned up at the collar, and a 1950s trilby hat, holding a brand new Kodak camera. He looks a bit of a mod. Rogers is wearing a Russian astrakhan hat and a magnificent, capacious tweed coat. He is beaming from ear to ear, not so much a technophile, like Foster, as an exotic.

I witnessed the force of Rogers’ personality in the run-up to his exhibition. Sometime over Christmas, he came up with a proposal that we might show an example of a prefabricated, affordable house he had designed in the Royal Academy’s courtyard at the time of the summer exhibition. The idea was discussed briefly at a meeting of our Summer Exhibition committee in January. Everyone was cautious or sceptical.

Rogers said that he might himself come and talk to the committee in February. He appeared, dressed in a fluorescent pink shirt and bright lime-green jersey (his signature colours). He made everyone feel that it would be an enormous privilege to show the house, irrespective of the practicalities. Everyone, who had previously been critical of the project, voted unanimously in its favour.

This is an enormous skill, to make others feel that it is a privilege to do something which they may think is impractical, and has almost certainly been translated into his success in competitions, which almost always involve an interview with the architect – in my experience of these interviews, lay clients are particularly susceptible to the personality of an architect – and in resolving subsequent, difficult issues of detailed design.

The second ingredient of Rogers’ remarkable success has been his ability to treat architecture in terms of the sociology of use. This was recognised early on at the Architectural Association, where his final report, signed by Peter Smithson, as well as by Michael Pattrick, acknowledged that “this student brings to the AA a capacity for worrying about the effect the building will have on people and a concern for shape on the inside, which has been an asset to his year”.

When at Yale, there was a difference in approach between the American students and the British, who included not only Foster and Rogers, but also Jim Stirling as a visiting tutor, and Eldred Evans, who Rogers regarded as one of his most talented contemporaries at the AA. The Americans regarded the British as too easy-going. They put up a poster which said “DO MORE”. The British responded with a poster which read “THINK MORE”. This was the essence of the difference in their conception of good architectural practice.

The third ingredient of Rogers’ success has been his highly innovative approach to the use of materials. Creek Vean, his first house, built from relatively traditional materials, was expected to be completed in six months, but eventually took three years. Not long afterwards, Team 4 was commissioned to produce a factory for Reliance Controls in Swindon. It was designed from ready-made components.

This idea of a building made up from pre-existing, industrial components as a kit of parts to be assembled, rather than constructed, was transferred to the Pompidou Centre and has thus avoided the use of the so-called wet trades, bricklayers and plasterers, who Rogers has generally found incompetent (or vice versa).

All his greatest buildings depend for their effect on the visibility of their means of construction, the idea that the building should not be treated as a finished object, but as a work of industrial assembly in which the imagination can readily grasp how it has been put together.

The fourth ingredient of Rogers’ success has been his talent for collaboration. Whenever he has needed someone to help him with a particular task, someone exceptionally talented has appeared. His first wife, Su, had a talent for organisation which enabled the office to win the competition for the Centre Pompidou.

His second wife, Ruth, as we all know, has a talent for cooking. Norman Foster was a stimulating partner early in his career. When he needed an engineer to help fill in the form which enabled him to win the competition for the Centre Pompidou, he selected the left-field, but brilliantly talented, Peter Rice, who was responsible for ensuring that the centre was built.

He has attracted talented people to work for him, to work out the details, to organise the office, including Marco Goldschmied, Jan Kaplicky, Mike Davies, Alan Stanton and Eva Jiricna. He has somehow made work fun; this, too, is a great talent.

The fifth ingredient in Rogers’ success is his sense of play. He is often categorised with Norman Foster as a pure, high-tech architect, a term which he detests. But, in fact, they could not be more different in their approach to design.

Foster reinvented the language of modernism by a strict adherence to visual and organisational logic. Rogers has always been more playful in his use of materials. The great drawing of the Centre Pompidou (or Beaubourg as Rogers always liked to call it) belongs much more to the world of Cedric Price and Archigram than it does to the world of Mies van der Rohe.

The Lloyds Building is full of architectural games – the grand-scale interiors full of concrete columns and escalators, the sinuous, steel external staircases, the extreme ingenuity of its ground plan tucked behind Leadenhall Market, the symphonies of lifts and pipes, and the small, blue toy cranes on the roof as if it is still under construction, although it is now Grade I listed and acknowledged as one of the great masterpieces of the late-20th century.

In the film of his work, which he made with Alan Yentob for the BBC, he describes several of his buildings, including the Lloyds Building and the Madrid Barajas airport as “fun”. It’s hard to imagine Norman Foster describing his buildings as fun.

The late Isi Metzstein used to divide architects between thin architects, who had a view of architecture as a problem-solving exercise, and fat architects, who understood that architecture was about the enhancement of visual and psychological pleasure. Under this definition, Rogers is a sybarite, seeing architecture as one of the pleasures of life, alongside food.

The sixth, and perhaps most important, ingredient of Rogers’ success has been his intuitive, as well as intellectual, understanding of the dynamics of the city. He has always understood that architecture is about more than space and shape and design.

It is about the orchestration of human interaction. Even as early as the Centre Pompidou, he allocated half the available ground space to an open piazza, which has been used ever since for performance art. The building originally had electronic signboards on its side, removed by Jacques Chirac who is said to have detested them.

After the failure of Rogers’ futuristic entry for the first competition for an extension to the National Gallery, voted both most popular and least popular by the public, he produced a design for Trafalgar Square for the exhibition which he, Stirling and Foster did at the Royal Academy in 1986 on London As It Could Be, which is not so different from the design which was implemented by Norman Foster in the late-1990s, and a proposal for a new footbridge across the Thames at Charing Cross, which again was implemented by Lifschutz Davidson in 2002.

He became an increasingly powerful advocate for policies which would revive cities, and particularly London, writing a joint book with Mark Fisher, the shadow minister for the arts, which was published in 1992 under the title A New London.

In the run-up to the 1997 election, he and Ricky Burdett organised a series of important debates about urban policy under the auspices of the Architecture Foundation, which he chaired. Following the election, he was asked to chair the Urban Task Force, which was responsible for the implementation of many of his ideas, including the appointment of a mayor, the introduction of congestion charges, the development of brownfield sites and open competitions for public buildings.

There are few individuals who have been so influential on urban policy. If, when I first encountered him, he exuded a more cosmopolitan air than the rest of London, then he, more than any other single individual, has been responsible for the transformation of London into a city of street theatre, bicyclists and localism, decentred, but metropolitan.

He realised long ago, from his upbringing in Florence, his visits to Barcelona and Rotterdam in the 1980s, and his holidays near Pienza, that a lively urban culture is essential to the development of the knowledge economy, in which the West End, with its theatres, squares and shops, and the East End, with its art galleries, are in their different ways at least as important to Britain’s economic development as the City itself.