David Baddiel, Menier Chocolate Factory

David Baddiel last did solo stand-up in 2004, when he walked out of a corporate gig after calling a bunch of bankers the c-word. Since then, he's spent his time mostly writing novels and doing some television and radio projects. It's his general absence from TV, he tells us in Fame: Not the Musical - an intelligent, witty and thoughtful examination of modern celebrity - that arouses pity in some members of the public who recognise him.

Baddiel first became famous as one half of two immensely successful double acts, firstly with Rob Newman and then with Frank Skinner, and acknowledges one big advantage of fame for a twentysomething single man as he then was; lots of fans wanted to sleep with him. "Aren't you worried that girls want to sleep with you just because you're David Baddiel?" he was asked at the time. "But I am David Baddiel!" came the logical reply.

But, as he quotes his favourite author John Updike, “Fame is a mask that eats into the face.” And, the comic adds: “Fame distorts every aspect of your life,” citing the example of his visit to Auschwitz, which was interrupted by a fan's question about when he might be doing more Fantasy Football.

By its nature the show is laden with starry names, but Baddiel drops them with aplomb and the anecdotes are well told and highly amusing - and almost all are at his expense. He recounts events at a showbiz party where there was a farcical series of mistaken identities, and how he's now convinced that Andrew Lloyd Webber is under the impression that Baddiel is Ben Elton (another bearded Jewish-looking bloke off the telly), while the composer's wife just thinks he's a rude git.

He talks about the inflexibility of a public persona – Baddiel went from laddish comic to smug north Londoner (racist code word for Jewish) without having a say in either matter – and how once you have been described in the media in a particular way, or the public has put you into a particular box, that's who you are for ever more. He examines the growing anti-semitism of modern Britain and the nasty underbelly of hatred that Twitter exposes on a daily basis; it's all done without rancour or an ounce of self-pity, but with lashings of good lines.

This show was first performed at the Edinburgh Fringe at an hour long and went by much too quickly, and now the extended version (nearly two hours with an interval) feels more rounded and satisfying. As well as interaction with the audience in the second half of the show (via tweets he has received from them in the break), Baddiel has added a few anecdotes – including a video clip that beautifully captures the perils of mis-speaking on live TV - and reworked the ending, taking out some of the schmaltz and adding a gloriously tasteless wank joke for his, er, big finish.

• Fame: Not the Musical is at Menier Chocolate Factory until 23 May