Few comedians arrive at the Fringe facing the sort of scrutiny aimed at Jim Davidson. It’s easy to forget he was once the mainstay of Saturday night television, a family entertainer who fronted BBC One’s primetime family game shows. These days his sporadic appearances tend to be overshadowed by accusations of racism, misogyny and homophobia, allegations further compounded by his arrest under Operation Yewtree. Charges against Davidson were dropped in August last year and he candidly details this experience for much of No Further Action.

The first half of his hour is straightforward stand-up and, from the moment he steps onstage, it’s clear he has the crowd in the palm of his hand. He kicks off with some painfully honest but very funny material about his alcoholic father before hopping around various incidents from his past. Little of his material is controversial bar some dirty jokes which simultaneously shock and delight a game crowd. On politics, he says he’s pro-immigration and he goes off on a rant to cement his credibility, a speech which isn’t so much a joke as an attestation against his detractors.

Demonstrating a surprising skill for mimicry, Davidson brings stories to life in a way that many comedians would begrudgingly envy, particularly when reminiscing about the former escapades of Freddie Starr (another comedian caught up in, and later released from, Operation Yewtree). However, halfway through the show things take a sombre turn as Davidson recounts the details of his arrest and the subsequent investigation. His frustration is clear (and understandable) but as he rakes over the coals he frequently dips into self-pity. His anger is still raw and he’s clearly seeking catharsis (and remuneration) by performing. Rounding things off with further anecdotes from his time on Celebrity Big Brother, it’s clear that that was an experience which had a profoundly healing effect on his cachet.

Push to one side any negative preconceptions you may have about Jim Davidson and he comes across as a solid old-school comedian. The stories are engaging and his jokes are precisely formed: after all, he’s been doing this for four decades. Perhaps, once he’s got the last few years out of his system, he might treat his fans to a full show of pure comedy.

Assembly Hall, 623 3030, until 25 Aug (not 18), 9.15pm, £13–£15 (£12–£14).