David Baddiel has lots of funny stories about trolls on the internet, and not being all that famous anymore; he was not all that famous even when he was famous, as he ruefully admits, recounting how, at the peak of his Fantasy Football League notoriety with Frank Skinner, he was mistaken by Andrew Lloyd Webber for being Ben Elton and therefore missed out on writing the libretto for The Beautiful Game.

This is Baddiel's first stand-up for 15 years, and a far cry in the intimate Menier, no doubt, from his rock arena sell-out days with Rob Newman. But he's far too clever not to be doing anything, and he's written three novels and the movie The Infidel, starring Omid Djalili, which is soon to be given a crowd-funded musical theatre production at Stratford East.

In this show, which is like a North London (but a little less Jewish) version of a Jackie Mason turn, Baddiel raps eloquently and entertainingly about most of these things, as well as his children, his partner, travelling on Ryanair and meeting Madonna backstage... and she didn't know who he was, either.

But he doesn't just reel off the anecdotes. The mistaken identity schtick with ALW develops into another mix-up over the composer's wives and the mishearing of a social introduction of The Edge as someone hanging around with Bono called "Reg."

So there's a narrative texture to most of what he says, and a wryly inflected acceptance of the ways of the world and his own small place within it. Even when he appears on a list as the world's sixth sexiest Jew, the downside is that he comes in just behind Alan Sugar at number five. Nothing is ever going to keep him happy and in a way that's quite appealing. Or, you may also feel, quite irritating.

He certainly ploughs this furrow of unease and discontent without ever crossing the border of panic or, equally, comic delirium. He invites interval tweets, using that material as another leaping off point, before showing a home video of his own daughter singing in a school concert; not so much bliss, as "bless." Nice, though, and Baddiel at last seems happy with what, and more importantly whom, he's got.

David Baddiel Fame: Not the Musical continues at the Menier Chocolate Factory until 23 May 2014