David Sedaris, Cadogan Hall

If such a thing were to exist, then American essayist, humorist and raconteur David Sedaris would be a Radio 4 superstar. His broadcasts on the channel receive hit numbers and are repeated regularly, and he's a permanent fixture on those parts of the literary festival circuit that its listeners flock to.

He's now touring the UK and it's sure to sell out, but it was interesting to see that his audience at Cadogan Hall was far more diverse than the channel's supposed typical listener – white, middle-class and 56 - might suggest.

An Evening With David Sedaris is a series of readings taken from his extensive oeuvre of books, essays, articles and diaries, and, as an American who now lives in Sussex, Sedaris is ideally placed to be an affectionate commentator on the foibles of those on both sides of the Atlantic. It's filled with his sly humour and there's just enough acid in his barbs to cut through what may at first appear gentle observations, delivered in his easy-on-the-ear lispy drawl. And besides, he's often the target for those acerbic asides.

Some of the exchanges with his fans seem too good to be true, but who cares when the jokes are this good?

Standing at a lectern and reading from his work – rather than memorising the material, or extemporising – Sedaris begins with an excerpt from his latest book, Let's Explore Diabetes With Owls, which is a collection of dramatic monologues he wrote for American high-school students. The one he chooses, Think Differenter, like all Sedaris's work, riffs on all manner of things, from the mentally impaired being able to buy guns in some American states, to the shortcomings of our memories and the annoying phrases that people use, such “I'll never forget when...” (which leads to a nice callback later).

Arabesque is a travelogue about his trip to the United Arab Emirates with an old girlfriend and Hugh, his partner of 23 years. In it Sedaris neatly – and very comically - describes how their liberal attitudes quickly abut those of their Muslim driver, and the American is refreshingly un-PC in his descriptions of their responses to what they see as his blinkered views. Company Man, meanwhile, which he wrote for The New Yorker, is a touching memoir of his family, masquerading as a simple story about having people to stay at his home.

But it's the last section of the show that's the funniest, as Sedaris reads from his diaries. I've no doubt that - as he describes with his journalistic work, which he edits several times before filing to an editor - he rewrites the events of his life. Some of the exchanges with his fans seem just too good to be true, but who cares when the jokes are this good? The subjects – including his leaking penis, which talks (“I'll make you regret you ever heard of khaki”), the worryingly weird way some parents threaten their children and a wonderfully filthy story about old people having sex – would never, ever be broadcast on Radio 4. And more's the pity.

Sedaris does a short Q&A and last night it threw up some interesting exchanges. The pace of the 90-minute show could be more varied – interspersing the long readings with the hilarious diary entries rather than delivering them all in one segment, for example – but this is a charming evening that ends on a very high note.

• David Sedaris is at Cadogan Hall until 31 March, then touring until 12 April