There's an air of frenzy about the efforts theatre managements are making, these days, to find good musical shows to fill Britain's big stages. Over Christmas the 3,000-seat Playhouse in Edinburgh strained every sinew to make a spectacular festive treat out of a touring production of Fame, which is essentially an unpretentious mid-scale musical with a deliberately downbeat setting and only a couple of memorable tunes. And in the wonderful world of tribute musicals - or any show designed to appeal to fans of a particular period in rock'n'pop - there seems no limit to the stretch that can be put on relatively small-scale shows, in the effort to push Britain's biggest theatres into those lucrative musical niche-markets.

From next Monday the Playhouse will be jiving again to the sound of a modest touring version of the essential late-1970s rock'n'roll musical Grease, which recently emerged - no doubt thanks to the determination of its organised armies of fans - as the surprise winner in Channel 4's Christmas countdown of the world's best 100 musicals. And this week at the King's in Glasgow, one of Scotland's largest theatres is playing host to the famous Boy George musical Taboo, first seen at a club venue in London two years ago, and now touring big "stage one" theatres all over the UK, including, later in the season, the 1,700-seat Festival Theatre in Edinburgh.

But if Taboo seems a slightly fragile show to be carrying so much commercial weight, this British version - not to be confused with the very different American rewrite that recently closed in New York - is by no means a bad night out for those with an interest in the recent cultural history of the UK, and in the music of the early 1980s. Created by Boy George himself with writer Mark Davies, and featuring a long playlist of 25 Boy George songs old and new, the show tells the story of Billy, a boy from suburban Bromley who escapes the clutches of his conventional home and family - Mum at the sewing machine, Dad slumped in an armchair nagging at his art-loving son to behave like a man - to make himself a new life in the city, among the gorgeous freaks and burgeoning New Romantics of the early-1980s club scene. Almost before his feet have hit the pavements of the West End, Billy has met Boy George, club organiser Philip Sallon, and the legendary high priest of camp self-reinvention, Leigh Bowery, all running around dressed like choirs of angels, camp Roman legionaries, or - in Bowery's case - large and scary pieces of conceptual art. And as the tide of sexual liberation and self-expression sweeps through the scene, and George and his band Culture Club rise to global fame, Billy begins to learn both about the positive creative energy that has been unleashed, and about the darker side of the story - the drug culture that almost destroys Boy George, the as yet unknown AIDS virus that eventually kills Bowery, and the homophobic violence that lurks on every street corner.

As a piece of theatre, Taboo has its weaknesses. The presence of the fictional character, Billy, can be confusing, since he combines his role as observer and outsider with elements of Boy George's own biography; the show is overlong at two hours a nd 40 minutes, and needs to lose a few of its weaker narrative songs, and shorten some others. But on the plus side, it boasts a committed and enthusiastic cast of 18, a four-piece band, a workable and effective cabaret set by Tim Goodchild, some excellent new songs (I particularly liked Bowery's high camp solo number Ich Bin Kunst), and two or three interesting central performances, notably from Stephen Ashfield as a fragile but charismatic George, Drew Jaymson as Philip Sallon, and a touching, thoughtful and outrageous Mark Little as Bowery.

What's most valuable of all about this show, though, is the serious attempt it makes, 20 years on, to understand what this strange cultural movement was all about, and what it meant to those involved. "I suppose I'm about the same age as Boy George," says writer Mark Davies, a fast-talking Liverpudlian in his early forties, "and when we met to work on the show, we got on really well. But musically, I would have been in a very different place from him back then; I had been very involved with punk rock, and I was more on the indie side of things by the early 1980s, I would have been listening to The Smiths rather than Culture Club. So when I first got to hear about these New Romantic people, swanning around in their fancy costumes and sipping their cocktails in Ibiza, I have to admit I thought, 'did we go through punk rock just for this?' In the play, George says that his world is all about style and fabulousness, and nothing to do with politics; and in that sense his movement was a reaction against the political face of punk, the anger and so on."

But as Mark Davies is quick to point out, if the personal is political, then Leigh Bowery and the young Boy George - in his famous pigtails and kabuki makeup - were clearly revolutionaries of a sort, dedicated to outraging every respectable norm of dress and behaviour, and, above all, to challenging gender and sexual stereotypes wherever they found them. "I think George would say now that elements of it were political," says Davies. "It was a great moment of self-expression, a celebration of a sexual freedom that was just about to be curtailed with the coming of AIDS. In the show we certainly look at the underside of that experience, and the casualties. But the show also offers hope, in the sense that if you see the light, as George did, and come through into some kind of maturity, then you can keep what was good from those times, and celebrate it, and move on."

• Taboo is at the King's Theatre, Glasgow, until 31 January; Festival Theatre, Edinburgh, 1-6 March.