Alexei Sayle was always the scariest alternative comedian. Rik Mayall and Ade Edmondson called themselves the Dangerous Brothers, but they were safe as houses next to this scouse skinhead. On The Young Ones, at the Comedy Store and in his own series Stuff, all those tirades about Thatcher, Oxbridge and Enver Hoxha rang not just funny, but insurrectionist. Now we know why. Sayle – according to his new memoir, Stalin Ate My Homework – was brought up believing in the violent overthrow of capitalism and mass murder as a political tool. His parents were doctrinaire communists, and young Lexi was raised to smash the bourgeois-fascist status quo.

Now 59, he's speaking about the memoir at the Edinburgh book festival and – while he's long left that ranting standup alter ego behind – bibliophiles may discern revolutionary fury behind the avuncular, man-of-letters persona. "He's still in here, that standup," says Sayle, chatting in a cafe near his home in Bloomsbury, London. "The delivery's all still there if I wanted to bring him out." I believe it. Sayle is a likable interviewee – but I find myself fearing the consequences of a stupid question.

But the book is written in a mellow tone. Sayle calls it a "satirical memoir", tracing life from birth to 17, with his dad, genial Joe, a railway worker, and his firebrand mum, a flame-haired Lithuanian Jew called Molly. It's a remarkable story, of infant limousine tours round Czechoslovakia, watching Alexander Nevsky at the Unity Theatre while his classmates queued to see Bambi, and arguments over breakfast about bureaucratic capitalism.

But how true is it? The adventures of young Lexi are so extreme, and so comical, one doubts it all happened as written. Sayle calls it "a compilation of sense memories. I wouldn't pretend it was entirely accurate." It's true to the spirit, he says, of an age he's proud to document: "The culture of the working-class autodidact. People like my dad are not much written about, compared to the lives and loves of upper-class people and their servants." But if it's true to the letter, that means Sayle's mum and dad were cheerleaders for murderous oppression. Molly, now in her 90s – to whom Sayle remains close – filed her own one-star review of the book when she heckled her son's reading in Crosby, declaring the memoir a "pack of lies".

Sayle admits to having found it "challenging" to address his parents' politics. "It's not my inclination to be condemnatory," he says – which may surprise anyone who's seen his comedy. "I just wanted to be honest. It's an affectionate book, but without shying away from the blinkered attitude we took in not looking at things that were wrong." What's interesting, he thinks, is that it's even possible to write fondly about supporters of Stalin. "You couldn't write a memoir of a loving Nazi family called Hitler Ate My Homework. Because they wouldn't be, I don't think. They'd just be fucking bastards, wouldn't they?"

The book is Sayle's first work of non-fiction. He gave up comedy in 1995 and has since published two volumes of short stories and three well-received novels. He's one of our most successful comedian-turned-novelists, but is bugged that no one takes novels by standups seriously. Even Stalin Ate My Homework "might have got more attention", he says, if he'd written it as a "misery memoir". He's been told by awards insiders that his novels are kept off shortlists "because of who I am, not what I've written. That is frustrating. But you very rarely get points for comedy. Unless it's Ian McEwan's Solar, which is so fucking ponderous as comedy, it's like an elephant being funny."

There's nothing diplomatic about Sayle, who – in this interview alone – burns bridges like a partisan. Blame the upbringing, but he manifests a palpable distaste for power and status, alongside a horror of toeing the party line. Yes, he's still active in leftwing politics, as a campaigner for Palestine, among other causes. But his commitment is far from total. "I was sitting on this panel with Tariq Ali and Bianca Jagger," he says, "and I thought, 'You fucking love this. For you people, this is tremendously satisfying.' I feel really ambiguous about the psychology of people trying to do good in the world. It's like Aung San Suu Kyi. I mean, you haven't seen your son, your husband died of cancer and you never saw him. Are you mad, woman? This dedication to a cause, it's fucked up." He pauses. "But on the other hand, the cause isn't helped by my ambiguity or qualms."

It must be tiring, this refusal to be a member of any club, and this frustration (I'm guessing) that life has complicated the "messianic sense of my own significance" with which domineering Molly equipped him. For a while, that sense seemed justified. In the late 70s, Sayle "invented" alternative comedy, he claims, as the first MC at the Comedy Store. ("It would have closed down if I hadn't been there.") But surely, I say, Marxism tells us that alternative comedy was historically determined, and the individual is irrelevant? "In dialectical terms," he agrees, "it would have happened anyway. But it might have had a slightly different character." Without him – "the only one out of all of us," he says, "who actually believed in [radical ideas]" – punk comedy would have been less rude, less wild and less Thatcher-bashing.

And as for standup at the Edinburgh festival – well, "I started that as well." That was 1980, when Sayle and Tony Allen staged the only comedy show on the fringe. "It was where I found my style," he says. "The first night I died. And I was so upset, I couldn't sleep."

But in Sayle, self-importance is at war with humour. He wants to be the best, while knowing that wanting to be the best is ridiculous. "I'm like the Soviet Union," he says, "which always used to claim it invented everything." Perhaps this contradiction will be resolved by an unexpected return to Sayle's first love, standup. He appeared at London's Royal Festival Hall in April as part of Stewart Lee's alternative comedy tribute night At Last! The 1981 Show. "And I fucking killed, mate," he says, beaming. "Walking on stage, I instantly felt: I know what this is. I felt a tremendous satisfaction just to be there." He has since "forced himself" as a mentor on several young comedians, and is planning to compere Robin Ince's Christmas show, Nine Lessons and Carols for Godless People.

This is exciting news for alternative comedy obsessives such as me – and for a standup scene sadly bereft of raving leftie outrage. It also represents a homecoming for the art's – and his parents' – prodigal son. OK, so he's not re-embracing communism, but he's making peace with the career that his extremist upbringing made inevitable. "My inclination for comedy came from being faced with so much pomposity and humourlessness when I was young," he says. "And now, I'm fascinated by that world again, a world I'd deliberately not looked at for 15 years. I'm fascinated by comedy."Alexei Sayle is at the Edinburgh Book festival on 13 August. Box office: 0845 373 5888. Stalin Ate My Homework is published by Sceptre and available through the Guardian bookshop, guardianbookshop.co.uk, for £16.