The conceit of drag girlband Denim’s show World Tour is that they’re performing it on stage at Wembley. Its achievement is to convince you that, were they to do so, they wouldn’t look out of place. They may not be performing to the 12,000 people they envisage in their heads, but they make Soho Theatre sound like that way, with this cheeky, characterful and vocally accomplished hour-long gig.

At the beginning, the five-piece seem too big for Soho’s main house. But then, that’s the joke: their swagger and stadium-pop touches are setting up a punchline to come. And you soon realise that only frontwoman Glamrou La Denim (Amrou Al-Kadhi) is outre in the conventional drag manner, and even her camp theatrics come with political edge. Her opening gag, singing the words “Alan Ayckbourn” in the style of a muezzin, are a mere palate cleanser for the solo routine mid-show, a sharp-clawed attack on attitudes to queer identity. It’s striking how transgressive this feels, as Glamrou retools Whitney Houston’s So Emotional into a cri de coeur.

Her bandmates, meanwhile, bring flavours other than fabulous spikiness to the table, and each gets her solo moment in the spotlight. Crystal Vaginova, she of the sparkling beard and cool, still demeanour, fashions Beyoncé’s I Was Here into something far filthier. Brittle Aphrodite Green, mother of six and with a marriage to Donald Trump under her belt, torch-songs Girls Just Wanna Have Fun. Electra Cute, the outfit’s Sporty Spice, blows the gaff on the Wembley conceit then redeems herself with a will-to-power rendition of Rise Like a Phoenix.

It’s all done with a great sense of fun – and a remarkably light touch given the bombastic, stadium-party-pop conceit – by the quintet who emerged earlier this decade as Cambridge University’s first professional drag band. Their act leans less on cattiness and on burlesques of femininity than is sometimes the case in drag. There’s also some lovely singing, solo and choral, all backed by a tight three-piece band. Scheduled in a 10pm slot, it could hardly be bettered for partygoers seeking a smart and uplifting late-night knees-up.

• At Soho theatre, London, until 3 February. Box office: 020-7478 0100.