“Why is Alan Cumming doing this?” asked a friend of mine, on hearing that the Scottish actor-singer was bringing his one-man cabaret gig to the West End. “Is he well enough known? Will people go and see it?” I must confess that I shared her pre‑show scepticism but wound up surprised and delighted by the quality on offer.

The cabaret genre is, to this cynic at least, almost always unremittingly excruciating. The performer croons a well-known song to within an inch of its life then follows it with some saccharine witter about the utter loveliness of everyone s/he’s ever met professionally. Cumming, mercifully, is having none of this.

The image of him on the programme cover, all rumpled in a same-clothes-next-morning way and teasingly biting a piece of rope, suggests as much. He’s led a colourful life, married first to a woman and now to a man, and grins like a mischievous imp while feeding us scurrilous titbits in between-songs banter that is intelligently witty and refreshingly well-crafted. That title, by the way, refers to the sentence he was asked to write down in his recent naturalisation test to become a US citizen.

And what songs he speaks in between. It’s a cracking selection of largely lesser-known numbers, which he performs with a rich, expressive voice that carries seductive traces of his lovely accent. Each number tells its own little story, and given that he sings so clearly, we find ourselves transported by the account of, say, the sexy Starbucks barista of Taylor, the Latte Boy.

Cumming is versatile, too, taking over with gusto at the piano from musical director Lance Horne for a Victoria Wood number then showcasing Next to Me, a tender love song he co-wrote. A cheeky nod to his best-known stage role, in Cabaret, comes via the Sally Bowles song Mein Herr (“I always said that I was a rover,” he pronounces with relish).

Most performers would have gone off the scale of the maudlin-ometer when referencing late co-star Natasha Richardson but here, again, he plays it just right. “This is for Tash,” he says simply, before starting to sing. This blue car is parked in London only until Sunday, so hitch a lift sharpish.

Opening night: Sir Ian McKellen and Alan Rickman show support for Alan Cumming

Until 6 September (0844 412 4663, www.iboughtabluecartoday.com).