Once in a while, you sense a change in the cultural atmosphere. It’s as if someone has flicked a switch in some distant room, and a process has begun: quietly, almost imperceptibly at first, but gathering pace and finally emerging into the open. When it starts to affect the buildings that shape our cities, then you know it is not going to go away. So it’s a big hello to the new postmodernism. This time round, it has more going for it.

The tectonic shift is apparent in two important new cultural buildings. The first represents the old regime: the celebrity art-dealer Jay Jopling’s gleaming £12m White Cube gallery in Mayfair. Designed by the low-profile Mike Rundell, designer of choice for the Brit Art generation, it is the ne plus ultra of ultra-reduced modernism. It is, for the moment, the end of a line. At the other extreme, you have the £12.5m Young Vic makeover in Waterloo. As recently as 2002, this temporary urban jumble, first conceived in the late 1960s, was going to be knocked down and replaced with a sleekly inappropriate glass and timber shoe box, designed by the steadfastly minimalist John Pawson. It would have been expensive and more than a little good-taste-corporate in feel. So the theatre had second thoughts and started again, looking to a younger generation. The result, by Haworth Tompkins, is revelatory.

In an extraordinary, almost alchemical process, the temporary Young Vic buildings, put up by the architect Bill Howell for £60,000 in 1970, have been breathed on, augmented, enhanced, layered. The place has been taken apart and put back together in permanent fashion. There is much that is new and some that is old. The miracle is that it is still, recognisably, the Young Vic. Although gentrification is reaching even unto this ragged part of the Waterloo/Blackfriars quarter, the theatre has kept its necessary rough edges and acquired some new ones. Let’s call it personality.

The low-budget feel is all there, too. Go into the administrative offices at the back and you find desks and storage made out of plywood, nuts and bolts — but done so well, you feel the system should be marketed as an alternative DIY furniture product. Graham Haworth and Steve Tompkins cut their teeth years back on a low-budget conversion of the old Ambassadors theatre for the director Stephen Daldry, while they limbered up to doing the Royal Court for him. They also built two dirt-cheap temporary theatres for the Almeida. These boys are jewellers of junk. Their fertile inventiveness is apparent all over the Young Vic.

But postmodern? Yes, but not as we used to know it. We all remember the excesses of the 1980s. In architecture, 99% of it was gruesome. It was essentially your standard modernist box with bits and bobs stuck on in the name of wit and historical reference. From that era, only one good postmodern building, and one almost good one, was built in the capital: respectively, the big fat hen of James Stirling’s No1 Poultry office building in the City, and the ziggurat- fortress of Terry Farrell’s MI6 HQ at Vauxhall. How things have changed.

The monumental decadence of 1980s postmodernism was purged by the recession of the early 1990s, after which a new generation of clean-cut modernists and minimalists — and Haworth Tompkins — emerged. But eventually, even pubs started going modern. The loft-living, polite-modern look, all steel, glass and polished wooden floors, has become every estate agent’s stock in trade. And whenever a stylistic movement gets down to high-street level, you know its days are numbered.

Thus, Habitat, under its creative director, Tom Dixon, has rediscovered variety and eclecticism: strong colours, patterns, textures. On the couture level, the achingly modish furniture company Established & Sons, run by Stella McCartney’s husband, Alasdhair Willis, also embraces the new eclecticism: his company’s Fold lamp — a traditional table-lamp shape pressed out of sheet metal — is pure postmodern. The style leader among Britain’s notoriously conservative housing developers is the award-winning Urban Splash. Impeccably modernist for years, Urban Splash has dived gleefully into postmodernism for the New Islington urban village in Manchester. With an apartment block like a pile of potato chips by Will Alsop, and social housing celebrating Dutch gables and Juliet balconies by inventive architects FAT, it is all wildly popular. Others are bound to follow.

The rejuvenated Young Vic reminds me a little of the early Californian experiments of Frank Gehry, using cheap timber and chicken wire. The main auditorium is clad in cement boards, each individually painted by the artist Clem Crosby. These are then covered by a screen of punched aluminium — like a scaled-up version of a cheese-grater. Tompkins explains that this is his equivalent of a theatrical gauze: opaque with the light in front of it, transparent with the light behind it. A simple and effective device that transforms the building between day and night.

But there is more going on here than just a clever architect doing ingenious things with cheap materials. The Young Vic approach embraces and reveals the past — such as the old butcher’s shop, and some of its tiling, which is still the main entrance to the theatre — while adding new spaces and layers of history. Tompkins is happy to let the building mutate on its own terms. He doesn’t do icon buildings. Not yet, anyway. And this is the difference between the new postmodernism and the old. This time, it’s far less superficial, far more intelligent and considerably less hysterical. We’re in for an interesting few years.