Never mind what’s hidden inside the wrapping paper, here’s a bigger mystery: how does Santa go down the chimney? Mac Barnett’s 2023 picture book of the same name appeals to inquisitive young readers by offering a festive selection of breaking-and-entering techniques. Does he find the key under the flower pot, post himself through the letterbox, even swim in through the taps? Jon Klassen’s illustrations feature a pack of reindeer, with inscrutable expressions, watching Santa’s increasingly wacky antics.

Directing his own adaptation for the Unicorn’s co-production with Told By an Idiot, Paul Hunter follows the book’s rhythm of a child’s racing imagination, with each far-fetched idea mooted, discarded, then swiftly replaced by another. He turns the book into a sort of variety show, with volunteers from the audience occasionally cast as Santa’s little helpers.

Designer Sonya Smullen has created a roof with a huge cutaway section that leaves the stage flanked by two snow-covered slides for the performers to slip down. In an exuberant opening number of a show that mixes rap, jazz, easy listening and folksy Danish songs, the entire set is transformed into a sleigh for Santa Claus Is Comin’ to Town. Smullen’s costumes are a jumble-sale mix of culottes, trapper hats and cosy dressing gowns, all evoking reindeer.

A cast of four (Giulia Innocenti, Nathan Queeley-Dennis, composer Frida Cæcilia Rødbroe and choreographer Mikey Ureta) divvy up the roles and take turns suggesting methods while the others act them out as skits, sometimes using puppetry. As you’d expect from Told By an Idiot, there are plenty of eccentric visual and sonic touches. Sound effects are visibly provided, Foley-style, and a giant snow boot is lowered from above like Monty Python’s giant foot.

By embracing a madcap, scattershot approach of styles, the adaptation loses some of the picture book’s gentler charm, and there is an inevitable hit-and-miss quality to the routines. They range from tired, including a section mimicking a razzle-dazzle gameshow, to inspired, as Santa straddles the photocopier to create a Flat Stanley-style version of himself. An interlude with a bonneted baby is more creepy than comical and there is a throwback music-hall vibe that sits a little oddly alongside additions such as Santa climbing into a Deliveroo driver’s giant bag.

If Barnett’s occasional rhymes and wordplay aren’t extended, then there is plenty of physical tomfoolery to entertain the audience of over-twos, including Santa being bashed down the chimney with tubes of wrapping paper to the tune of jingle bells. The biggest laughs come from the panto perennial “he’s behind you”, deafeningly delivered by today’s young audience. Maybe Slade’s granny is right and the old ones really are the best.

• At Unicorn theatre, London, until 3 January