^‘I can see that, as a body of writing, it is a rag-bag of styles and genres,” Michael Rosen once said of his work. “But does it matter? I’m not trying to hoodwink anyone. I’m not trying to gain membership to a Peerage of Poets. I write ‘Bits’ and ‘Stuff’.” As always, the future children’s laureate was being both modest and a little feisty. Still, it’s a good description of So They Call You Pisher! It’s a mishmash, at once merry and pensive, of personal memoir, a history of left politics in postwar England, a portal into a lost Jewish London and a portrait of the artist as a nervy young man.

Famous individuals flicker in and out of the narrative – among them Christopher Hitchens, Howard Marks and Clive James (the latter yelling, “I’ll fucking have you! You’re ruining everything I’ve ever worked for!” when Rosen fluffs lines at a student revue audition) – but at its heart are his parents Harold and Connie Rosen. Harold was a poet, a noted educationalist, author of Are You Still Circumcised? (1999), and treated by some contemporaries “as if he was a cross between Lenny Bruce and Isaiah Berlin”. He and Connie met at a Young Communist League meeting in 1936 and both fought against Oswald Mosley’s fascists in the battle of Cable Street that year.

Willy Goldman, author of the timeless East End My Cradle (1940), described himself as “forever a prisoner in this not too tender trap. I can never escape from it and I would never want to.” Unlike his parents, Rosen grew up on the opposite side of London (“1950s Pinner was not the most encouraging place to start a branch of a political organisation aimed at world revolution”), but he absorbs and makes his own stories about the radical, rambunctious East End: women leafleting for rent strikes, live chickens on Hessel Street, dray horses skidding on the winter ice, “old migrants, sailors from all over the world” sitting in Whitechapel library while “talking about ‘the heim’ and politics and playing dominoes”.

The secular Rosens dreamed of another world too. They chose or cut off friends according to their politics. They read the Daily Worker assiduously, brought home books from Moscow’s Foreign Languages Publishing House, went on camping trips, and took holidays in eastern Europe. “They were yearning,” Rosen writes, “for something bigger and more universal than freedom for Jews alone: it was the liberation of all humankind they were after.” That’s also why, he believes, they were so disappointed when he chucked in his medical studies at university: “It seemed to them that it was the most worthwhile of all professions, devoted solely and selflessly to the benefit of others.”

So They Call You Pisher! is full of holes and absences – the homes and homelands of so many Jewish refugees; Rosen was 10 before Harold told him about an older brother who, aged just one, “coughed to death in your mother’s arms” – but it also brings to life countless epiphanies and emergences: Beyond the Fringe; Michael Foot on television; holidaying with French teenagers; Eric Hobsbawm drawing connections not just between political situations across European nations in the 19th century, but between politics and Beethoven; Joan Littlewood’s production of Oh, What a Lovely War!; and, when hearing Dylan, being agog at the way he had “invented a way of singing that sounded as if it was talking”.

Sound is at the centre of Rosen’s book. It rings with ribald Yiddish phrases, vividly remembered parental warnings (“Don’t eat the corned beef!” “Take the chicken!”), the triumphant choruses of folk and blues songs roared by Aldermaston protesters. It speaks eloquently about the impact of discovering the work of Gerard Manley Hopkins with its “jazzy, jerky feel” and “the free verse, ‘proletarian’ poems full of dialogue, proverbs and slang” of American poet Carl Sandburg. Best of all is a tribute to the Beatles – not their music so much as the wit and cross-fire repartee with which they peppered their interviews. I chuckled at his recollection of Maurice Bowra, classics don and warden of Wadham College, Oxford, trying to engage with students at high table: “Mmm, Ceylon, I was in Colombo. Walls. Very fine walls.”

Rosen has spent much of his life writing poetry that charms younger readers, and also advocating for inclusive, experimental approaches to mass education. The formative episodes of his youth include losing touch with a junior school friend who failed his 11-plus, and an exchange scheme with Winchester College, whose students he envies on account of the more adult and less formalist approaches to literature to which they’re exposed. He recalls studying Far from the Madding Crowd, about which a teacher asked, “Hardy. Mmmm. Optimist or pessimist?” Rosen himself is a bit of both – by turns tender and tetchy, antic and subdued, always keen to preserve disorder.

• So They Call You Pisher! A Memoir is published by Verso. To order a copy for £14.44 (RRP £16.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.