The Tailor-Made Man, Arts Theatre, London

Bradley Clarkson, Faye Tozer, Mike Cotton and Dylan Turner in The Tailor-Made Man (Alastair Muir)

This new musical bursts onto the stage like a wittily knowing and colourful cross between Mack and Mabel and Hollywood Babylon. It tells the fascinating and ultimately rather heartening true-life story of William “Billy” Haines, one of MGM's biggest stars in the late Twenties, though a heartthrob who did little to hide from his employers a decided offscreen preference for men.

When he was busted while having sex with a sailor in downtown LA, Louis B Mayer ordered him to enter into a sham marriage with Pola Negri, the redoubtable Polish silent screen diva. Haines refused, choosing to live openly with his long-term and long-suffering partner, the set painter and stand-in, Jimmy Shields. He was blacklisted; his acting career was in ruins; and there was a hideous gay-bashing incident based on a misunderstanding. And that is where bigots would like the saga to conclude.

But with a delectable mixture of cheek, talent and conscious irony, the now non-person and his lover bounced back as hugely successful interior designers in Hollywood – providing the glamorous surfaces that they knew only too well hid a multitude of sins.

I like the way that the show, directed by Claudio Macor who co-wrote the almost over-snappy book with Amy Rosenthal, zestfully lays into the grotesque hypocrisies and homophobic double standards of Tinsel Town, without falsely romanticising Haines or pretending that he was more interested in crusading than in compulsively cruising.

Even in Dylan Turner's personable and well-sung portrayal – and with Bradley Clarkson's fine performance giving sympathetic substance to Jimmy's troubled devotion to him – Haines remains nobody's idea of noble hero. But the point here is that nor were the majority of straight (or supposedly straight) stars who got away with their hair-raising private behaviour by toeing the official line.

The flashback structure has its clunking moments but the droll, savvy, intricately rhymed pastiche songs by Duncan Walsh Atkins and Adam Meggido tip the wink trippingly, whether in references to “doors that swings both ways” in a wonderfully insinuating song about designs, interior and otherwise in the homes of Hollywood luminaries, or in a ditty that gives Mike McShane's very funny Louis B Mayer the chance to profess his supremely disingenuous belief that MGM is just one big happy “Family”.

Faye Tozer is brassily ebullient as Marion Davies and has great chemistry with the male leads. As Rupert Everett occasionally reminds us, the Celluloid Closet is still the canniest option for a gay actor in Tinsel Town, so it's good that this story of non-conformity that culminates in a kind of victory is getting a rare outing.

To April 6; 0207 836 8463