Fat has grown up. From the enfant terrible of British architecture, designing underground nightclubs in early 1990s, the architectural practice (full name: Fashion Architecture Taste) is now planning a retrospective of the influence of modernism on housing for the elite Venice Biennale. But after two decades of bringing fun and creativity to building design, the party is over. Venice will be its last project.

"As an architectural practice, Fat was a bit more like a band," says co-founder Sean Griffiths. "I think because our work is seen as quite controversial it meant that we were always interesting, but we were never likely to be the next Richard Rogers. We came to the conclusion we would be doing more of the same and perhaps it was time to think differently," he says.

Griffiths is to take up the post of professor of architecture at the University of Westminster. It's a homecoming: Fat was born out of the institution after two students, fearing for their employment prospects in the recession of the early 1990s, collaborated with their tutor to launch the practice. "I decided I could either be on the dole or be on the dole and have an architectural practice. It would be very difficult to do that now. I had cheap housing, but for about a year I was on benefits. It allowed me to start a business which over the years employed 25 people."

It's not just the end of a creative cycle that has forced the group to reassess; commercial pressures have taken their toll, too. Griffiths says today's construction industry, controlled by the behemoths of development, has pushed out small, innovative practices like his.

"It has actually made it extraordinarily difficult to be a small, high-design practice. Both in the private and the public sector, the question that's never asked is: are you any good at designing things? They're interested in your turnover, they're interested in your resourcing, they're interested in box ticking. The people who tend to win projects are people who are good at filling in those forms."

Add high land prices into the mix and it's a recipe for failure: "The more that you spend on the land, the less you've got to spend on the quality of the build," Griffiths bemoans. "It's a shift away from the core thing we do as architects to a business-orientated approach and I think that's actually reflected in the built environment."

As a result of these pressures, Fat had relatively few opportunities to work with social housing providers. ("They go down the route of least resistance because there's no incentive to do otherwise," he says. "That's an issue we're going to face if we ever do get around to building houses: the race to build them drives down quality.") Its primary housing project – New Islington Square in Manchester, working with Manchester Methodist Housing Association – is fondly remembered as the archetypal regeneration project of the Blair years.

"Part of the idea was this notion of the creation of places and new, vibrant optimistic architecture. Part of that was to make a statement: look what we're doing, we're not building dowdy old houses, this is the future," Griffiths says. He enjoyed the project for the time it offered to work with residents, sharing their ideas and aspirations and translating that into the design. But when the regeneration funding stream dried up, so did opportunities for small practices like Fat.

Griffiths is critical of the way major development schemes, tailored to the financial property market, have failed to meet urgent housing need. "You get identikit developments because people who buy them don't buy them as a home, they buy them as an investment," he explains. "A huge development is marketing its properties to the Middle East, the Far East, to Russians, to the Chinese. I just find that astonishing that we are allowing that to happen. That is the unfettered free market, and the result is that it adds to house price inflation and these people don't even rent the properties out – they sit on them. It offers nothing to London whatsoever."

His answer? "Tax the fuck out of those people to generate some revenue that you can re-invest in social housing and to disincentivise the thing in the first place. The so-called private sector free market is not working; it's not delivering what we need."

Despite his anger, Griffiths remains positive about the future – largely thanks to his students. "The sheer talent and skills that these people have is mind-boggling. They are just so talented and committed," he says. He also perceives a commitment to better housing design.

"Young architects are people who are on the receiving end of the current housing crisis. They are people who would like to be living in secure, affordable, well-designed houses," he says. "Yes, they are interested and the younger ones are slightly less cynical. They haven't been through the machine where they think, 'Let's do what the developer wants so we can pay our staff this month.' "

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