One afternoon in the early 1980s, Tariq Ali, wearing only a towel, leapt into a room in Private Eye’s Soho offices. His mission was to liberate the magazine’s editor, Richard Ingrams, from a tiresome interview with Daily Mail hack Lynda-Lee Potter. “Mr Ingrosse, sir,” said Ali, posing as an Indian guru, “Time for meditation. Please remove all clothes.”

It’s a terrible shame Potter is dead because I’d love to have heard her side of the story. Did she, as Ali reports, nearly faint before making her excuses and leaving? Was she taken in by the ruse that concluded with Ingrams and Ali giggling over pastries in the nearby Maison Bertaux? Or did she, as seems more likely, immediately recognise Britain’s foremost Lahore-born, Oxford-educated Trotskyist intellectual, after whom the Rolling Stones reportedly named their song Street Fighting Man – if only from his fabulous moustache? We will never know.

“There have been other versions of this story,” Ali tells us on page 107. “This is the only one that bears the seal of total accuracy.” It’s a line that typifies this entertaining, politically engaged and yet exasperatingly self-justifying 800-page book in which, as is obligatory in the autobiographical genre, the author marks his own homework and gives himself an A+.

Earlier this year I reviewed Liz Truss’s infinitely more awful memoir and called it an unwitting update of Trollope’s He Knew He Was Right. Boris Johnson’s memoir eclipses both Truss and Ali in it’s lack of humility or self-critique. But the point remains: for all that Tariq Ali is clever, cultured and good company in this book, he is not a mea culpa kind of guy.

There’s a very long chapter about a bitter coup at the New Left Review’s editorial board on which Ali served, that had even me, someone who’s written two books for the NLF’s book publishing arm Verso and so might be expected to find such stuff enthralling, wondering if I had the upper body strength to heft the book across the room.

He also reproduces correspondence with the late, great historian EP Thompson about NLR office politics when, actually, I’d have much preferred the pair to have discussed the unmaking of the English working class in Thatcher’s Britain. No matter. Ali ploughs on, settling scores even though the protagonists are long dead or have sensibly forgotten what got them so vexed at the time.

Lenin wrote that left-wing communism was an infantile disorder; Freud described the narcissism of small differences; Monty Python skewered the Trot tendency to expend energy on internecine conflict rather than overthrowing capitalism: Ali has learned too little from each.

And yet, I couldn’t avoid feeling nostalgia for Ali’s glory years as a broadcaster in the 1980s when he would write a screenplay about Spinoza and then visit Derek Jarman in Dungeness to check on how the ailing director was doing with his Wittgenstein biopic. This was the era that Ali and Trinidad-born broadcaster and activist Darcus Howe collaborated on making the unprecedentedly ardent and ethnically diverse cultural and current affairs show The Bandung File for Channel 4.

He starts his book in Southall, west London, in 1979, being thrown down town-hall stairs by cops during the same demo against the National Front in which New Zealand teacher and Anti-Nazi League supporter Blair Peach was killed by an officer from the Met’s notorious Special Patrol Group. At the time, Ali was standing as the International Marxist Group’s candidate in the general election that would bring Margaret Thatcher to power.

I shook with outrage reading Ali’s description of the demo’s brutal suppression. He writes that he and like-minded anti-racists, including reggae combo Misty in Roots, were roughed up by the police and then processed through a racist court system. Forty five years on, is Britain any less racist and the state any less corrupt than it was in the terrible era Ali describes?

Ali mutates from street-fighter to Trotskyist Zelig, popping up everywhere. After Southall, he finds himself interviewing Indira Gandhi, advising her that Pakistan was unlikely to invade Kashmir. He witnesses the fall of the Soviet Union, strikes up a friendship with Hugo Chávez, is a founding member in 2001 of the Stop the War Coalition and concludes with a passionate analysis of Gaza. For all its flaws, it’s a superbly bracing world tour, written by a historical materialist who turned 80 during the book’s composition, in which he is often insightful and usually correct in his analyses.