Andrew Lloyd Webber has taken over the St James Theatre and turned it into The Other Palace, a try-out home for musicals, with a remit to develop new shows, under the artistic direction of Paul Taylor-Mills. The first production, The Wild Party, may not be new, but it makes for an appropriately sparkling opening bash.

Michael John LaChiusa's musical, first seen on Broadway in 2000, adapts a Joseph Moncure March 1928 narrative poem about a Manhattan showgirl named Queenie who hosts a debauched party. Queenie - Frances Ruffelle - performs nightly in a vaudeville show, alongside her lover, Burrs, who has a sinister-from-the-off clown act. The Wild Party, a la Chicago, dips into vaudeville turns to help tell its story of a party that gets out of control.

It might not boast memorable individual tunes, but there's a really gorgeous jazz score, that murmurs seductively under the (rather lacklustre) dialogue and bursts into syncopated, scorching song and dance numbers, from scatting be-bop and the black bottom, to blues and the odd ballad. Under Theo Jamieson's musical direction the band is smoking hot, and under Drew McOnie's direction and choreography, the cast respond with flapping, high-kicking, jazz-hands-ing joy.

A particular treat are the synchronised, slow-shuffle moves of a pair of young black performing ‘brothers', Gloria Obianyo and Genesis Lynea. Their number "Uptown", about how as the twenties roar, Manhattan is becoming a melting pot of black and white, straight and queer, is a highlight.

Although staged with aplomb, the storytelling beats of the musical itself can plod, especially in the first half where each character's backstory is established; funnily enough, it's when the bathtub gin starts to flow that the show does too… Recreating drunken depravity onstage can feel cringe, but here the cast are convincing whether cavorting in bath tubs, Charlestoning into each other's arms or rolling around on a bedstead. The wilder it gets, the better: pacier, punchier.

The second half, naturally, also comes to show us the vacuity of this hard-partying, adulterous lifestyle – the emptiness behind the glitz, the come-down after the come-on. But the show itself, underneath its own enjoyable razzle-dazzle, is similarly lacking. Suggesting that getting smashed and sleeping around might just be a way to fill a hole is hardly revelatory, and there's not much heart or depth. Even Queenie, while played with a winning mix of sugary sweetness and sultry sexuality by Ruffelle, remains shallow, all surface.

There are still plenty of fun performances: Bronte Barbe is comically gauche as a Poughkeepsie girl agog at the big city, while Melanie Bright is amusingly vacant as a smacked-out artist. Bringing a welcome sense of danger to proceedings are Dex Lee as Jackie, a smouldering dandy with an insatiable appetite for sex and stimulants, and John Owen-Jones as Burrs, who has a seething resentment and volatile fire within him. In truth, given the nasty turns it will take, the production could do with more rough edges.

It looks gorgeous, on every front: designer Soutra Gilmore has had a fine time costuming these flappers and dappers with feathers and fringing, velvet and sequins. The set is a persuasive mix of the theatrical – an arc of stage lights, a stripy floor - and the domestic - wooden banisters, a wheeled-on bed. And the whole thing is really beautifully lit by Richard Howell, combining stagey limelight with woozy party atmospherics. Not a revelatory show, or a musical that feels desperately urgent, but The Wild Party is nevertheless a fizzing way to toast this new venture.

The Wild Party runs at The Other Palace until 1 April.