Nevertheless, she persisted. That old millennial feminist rallying cry springs to mind repeatedly on reading Diane Abbott’s absorbing new autobiography, which describes a life of astonishing resilience. Her teachers thought a working-class black girl wouldn’t get into Cambridge, but she persevered and proved them wrong – only to be mistaken at one college ball for the hired help. She battled through multiple rejections before finally landing the Hackney seat that made her Britain’s first (and for many years only) black female MP, and then through the impossible pressures of being a single mother in parliament in the days of endless late sittings and no childcare. (Once, in desperation, she voted with her two-week-old son strapped to her, only for a Tory MP to complain that it was bad enough having David Blunkett’s guide dog around, never mind babies.) Frozen out by Neil Kinnock, Tony Blair and Gordon Brown for her uncompromisingly leftwing views, she was sacked from her first frontbench job under Ed Miliband (which she secured by running unsuccessfully against him for the leadership) for publicly attacking his immigration policy.

But nevertheless, she persisted, staging a late comeback as shadow home secretary under Jeremy Corbyn only to be forcibly “stood down” from his 2017 election campaign after a fumbled radio interview. (She was ill at the time, she writes, and only learned of her unceremonious benching from the media.) Through it all she has endured decades of horrific racist and misogynistic abuse, only to lose the whip herself for a shockingly ill-judged letter sent to this newspaper implying that the “prejudice” suffered by Jews, Irish people and Travellers was not the same as the racism endured by black people. Yet here she still is, triumphantly re-elected aged 70, despite Keir Starmer’s best efforts. Whatever you make of Abbott, the story of what she overcame to get here offers fascinating insights into both the overtly racist Britain of her childhood – when young men would go door to door seeking black families to beat up – and the sometimes flawed but compelling politician it produced.

Born in 1953, in London, to parents who had both emigrated from Jamaica, even as a child she was impressively self-confident. Her factory worker father’s fierce aspirations for his family drove a move into what was at the time very white suburban Harrow, while Diane was sent to grammar school. But he was also domineering and oppressive, venting his frustrations on his wife – who eventually left him – and the children she left behind. He made her mother’s life miserable, she writes, yet bequeathed “a stubbornness and determination that helped make me the woman I am”.

Abbott writes with empathy and nuance about this complex inheritance, which left her estranged from her father and temporarily from her younger brother too (though the siblings later reconciled). As a child she hated her father’s controlling behaviour, she explains, but now she sees in it the consequences of a society that humiliated Black men: “Because Daddy could not vent his anger and pain about the racial indignities he had to put up with in his workplace or in the outside world, he brought that rage home.”

It was feminist and civil rights causes that first caught her interest and though she joined the Labour party after university, while working somewhat unhappily as a Home Office civil servant, she could have drifted away from mainstream party politics had it not been for an early boyfriend. Abbott is kind but very funny about the young Jeremy Corbyn, describing a booze-free Christmas of “true socialist frugality” in his family’s freezing house, and his idea of a hot date (visiting Karl Marx’s tomb). There’s nothing joyless or sanctimonious about a politician who admits that as a young woman, she got a job in television on the suggestion of the married TV executive she was then sleeping with.

Yet A Woman Like Me paints a picture of her as always slightly on the outside, even of the close-knit socialist circles in which she has so long moved. Some of the subtler slights she describes – when working in the 1970s for the National Council of Civil Liberties, or on the Marxist magazine The Leveller, or even in Corbyn’s shadow cabinet – will, I suspect, resonate with many women and minorities who have worked in progressive institutions that don’t always live up to their egalitarian ideals.

This isn’t the book for anyone seeking juicy political gossip, or indeed deep reflection on why Labour lost two general elections in a row under Corbyn. (Though she concedes there was “some weight” to concerns about the party’s handling of antisemitism complaints, she also suggests they were weaponised by his critics: similarly she admits the letter that cost her the whip was “clumsy” but feels harshly treated compared with other MPs who caused offence.) More surprisingly, A Woman Like Me is also light on concrete achievements. We hear all about what she stands for – women’s rights, humane immigration policies, tackling poverty or Black boys’ educational underachievement – and what she wanted to do as a frontbencher under Miliband or Corbyn. But there is less about what she actually did, beyond a few pages about convening victims of the Windrush scandal or visiting female refugees in detention. Instead, there are dark hints about leftwing comrades “who could not get their heads around the idea” of a black female home secretary, or about some shadow cabinet colleagues’ disappointing reluctance to discuss foreign policy or her opposition to nuclear weapons (though neither were part of her brief). In 2017, she seriously considered retiring.

Well, perhaps having a new Labour government to rebel against will give her a new lease of life. For it’s the chapter describing her barnstorming backbench opposition to the 2008 counter-terrorism bill that feels like the real emotional heart of this book; the rebels lost, but she won the Spectator’s parliamentary speech of the year award for going down fighting. Nevertheless, she persisted. Readers embarking on this rich, complex memoir will be rewarded for doing the same.

• A Woman Like Me: A Memoir by Diane Abbott is published by Viking (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply