Audrey Hobert opens her Berlin show standing on a ladder hidden inside a comically overlong beige trenchcoat, wearing Groucho Marx joke glasses with orange-fluff brows and moustache matched to her strawberry blond hair, and miming a prop banjo while singing "I Like to Touch People," a peppy song about charming strangers.

That opening bit, staged at Huxleys Neue Welt, distils the 27-year-old pop star's approach: the trompe l'oeil of high-budget pop stagecraft remade as slapstick. When the lights dim after the number, Hobert climbs down and swaps to a regular-sized trenchcoat. The changeover is entirely visible, yet the lights come back up as if to say "Hey presto!"

Backstage before the show, Hobert gives a tour of her dressing room. On her second time outside the US, the novelty of having local snacks on the rider has not dimmed, though her enthusiasm for chocolate thins cannot distract from the props around the room. Two sets of joke-shop Groucho Marx glasses sit on the dressing table, their original black brows and moustache replaced with orange fluff.

"Those glasses are not flattering," says Hobert. Having matching hair under the giant plastic nose, she says, "makes it more flattering."

Hobert built her name as co-writer of Gracie Abrams' hit album before striking out solo. Her funny, wordy songs have since won her a fervent cult following, and an interview series with the Guardian has dubbed her the Steve Martin of pop — a comparison that captures the blend of smart writing and physical comedy in her live performance.

As her tour reaches the UK, Hobert has been explaining why imperfection matters so much to her in pop. It is a principle visible in her staging choices: visible costume changes, joke-shop props and a prop banjo in place of polished choreography. The approach deliberately punctures the seamless illusions of mainstream pop production.

The Berlin date shows the formula in practice. A concealed ladder, an oversized trenchcoat puddling on the dressing-room floor, a spoof disguise — each element takes a convention of arena-scale pop and hands it a punchline. The wordy charm of songs like "I Like to Touch People" carries the same sensibility into the writing itself.

With UK dates now underway, Hobert's blend of verbal wit and visual gag looks set to win over audiences far beyond the cult following she has already gathered.