In early 2015, a couple of months after his mother died, David Baddiel wrote to his younger brother, Dan, a sometime taxi driver in New York, setting out his plans for “a warts-and-all stage show” about their parents’ lives, and asking if he had any objection to the idea. Dan sent him a one-line reply: “You’re not doing it.” The comedian’s elder brother, Ivor, maybe knew him a little better. When Baddiel explained what he had in mind, Ivor simply said: “We could talk about this for two hours, and go back and forth on it, but I may as well just ask you upfront, are you going to do this?” To which Baddiel said: “Yes”.

The show, My Family: Not the Sitcom, had a sold-out run in the West End and toured the world. All of his brothers’ misgivings were entirely justified. In a revival at the Royal Court, the official publicity called it “a massively disrespectful celebration of the lives of David Baddiel’s late mother, Sarah, and dementia-ridden father, Colin”. He liked to describe it as “a twisted love letter” to his parents, a two-hour monologue in which he detailed, with slides and documentary evidence, every sexual secret of Sarah – and Colin’s extreme mental decline. This is the book-length version of those revelations.

In between the live performance and its publication, Baddiel has written his thoughtful polemic on the history of antisemitism on the left, Jews Don’t Count, and, to begin with here, you half expect a second personal chapter of that argument. His mother was born in Königsberg, in Germany, in 1939, and escaped with her parents to England only after her father had been interned in Dachau, before it became an extermination camp. The previous generation of his father’s family, meanwhile, had escaped the Cossack pogroms in Latvia to settle in Swansea. Those tragic dramas serve only as a preface to the high domestic farce that follows, however.

His mother – “the Erica Jong of Dollis Hill” – is, to begin with, the star of this north London suburban show. There were three people in her marriage to Colin and, in the best traditions of the 1970s, the third wheel was a bearded and pipe-smoking Lothario who was a big cheese in the golfing memorabilia world. Sarah had an obsessive and barely concealed affair with David White for 30 years or more. The giveaway was the fact that, having never previously showed an interest in links and fairways, she set up a rival golfing memorabilia business to her lover’s, and gave it the same name, Golfiana.

Baddiel insists that he has a fatal flaw in regards to this history: an “on-the-spectrum need to tell the truth”. Thus he provides every toe-curling detail of his mother’s ardent trysting, documented in emails and love poems and Kodachrome, discovered after she died. Part of his justification for this private “reincarnation” is that he believes it is what she would have wanted. She was, for example, “accidentally” in the habit of copying him and his brothers into her correspondence with White, as if to provide evidence of her thrilling libido. Here’s one example, written when Sarah was 65: “The leukaemia (and now also the Crohn’s Disease) makes me very tired, but perhaps you can join me to make the ‘naps’ more interesting!!!” Baddiel finds solace, and extra laughs, in being at least as concerned by the wayward punctuation of those remarks, as by their sentiment.

If this was only a book about his mother’s vivid sex life, it might feel a little bit too creepy. The fact that it is not a one-woman show but a double act, however, often also gives it an unhinged poignancy. Sarah has her surreal match in husband Colin who, having taken redundancy from the biochemistry labs of Unilever, where he researched deodorant, makes a living buying and selling rare Dinky toys (in a stall at Grays antique market opposite her Golfiana). Colin, apparently, remained unaware of his wife’s semi-secret life, though it perhaps explained his explosive irritability. An atheist, his typical response to any form of Jewish family ritual was to interrupt prayers to say: “Can we finish the fucking ollywollybolly and eat now?” And that was, it seems, about as polite as Colin Baddiel ever got.

As his dementia advanced in later life, he became more and more uninhibitedly Colin. A standup comedian’s prose can rarely resist a payoff one-liner in each paragraph, but in exploring the tragedy of his father’s condition, as well as the dark comedy of his marriage, Baddiel finds a range of complex registers to describe the baffling conundrum of a man who no longer knows his son’s name but can still beat him at chess.

At times, understandably, Baddiel questions the ethics of his fabulous confessional, that old notion that “once a writer is born into a family, the family is finished”. But he convinces you, too, that comedy writer was really the only career option that his parents’ marriage reasonably allowed him; and, in that spirit, he does them proud.

• My Family: The Memoir by David Baddiel is published by Fourth Estate (£22). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply