Eleanor Marx photographed c1875 Eleanor Marx: A Life, by Rachel Holmes, Bloomsbury, RRP£25, 528 pages

Eleanor Marx joked that she had inherited her father’s nose but not his genius and, if she anticipated that it was her fate to be overshadowed by the author of Das Kapital, then she could only be proved correct. Yet contemporaries who knew her work as an activist, writer and translator would have protested nonetheless at the injustice. Now, in Rachel Holmes’ fine biography, we have all the evidence we need to revise this modest self-assessment.

Eleanor was born on January 16 1855 in a two-room garret in Dean Street, London, the sixth child of Karl Marx and Jenny von Westphalen. Only two of her siblings survived into adulthood – her sisters Jenny and Laura, 11 and 10 years older than her, respectively. The eldest son, Edgar, died of tuberculosis 12 weeks after Eleanor’s birth and from that point her father seems to have invested all his hopes and affection in the family’s most recent arrival. He and Eleanor would be soulmates until his death in 1883.

One consequence for Eleanor, known throughout her life as “Tussy”, was that her education was almost entirely conducted at her father’s knee. She barely attended formal school – in part because the family was always so short of money, surviving for periods on money raised by pawning linen and jewellery, or on generous handouts from Karl’s collaborator Friedrich Engels. Instead, she learnt French and German from her French-speaking older sisters and German-speaking mother, while her father encouraged his own love of “book-worming” in her from as soon as she could read.

Karl introduced her to Shakespeare, to the English, French and American novel, to Scott, Balzac and Fielding. He encouraged her writing and love of the theatre. Years later Eleanor recalled: “He would, all unconscious though she was of it, show his little girl where to look for all that was finest and best in the works, teach her – though she never thought she was being taught, to that she would have objected – to try and think, to try and understand for herself.”

And while Karl laboured on Das Kapital he found time to include Eleanor, extracting “examples and narratives that could be turned into enjoyable stories and useful instruction for his little girl”. As Holmes puts it: “To say that Eleanor Marx grew up living and breathing historical materialism and socialism is therefore a literal description and not a metaphor.”

Holmes, a cultural historian known for her biographies of Victorian subjects, here builds a vivid picture not just of Eleanor Marx but also of Karl Marx, Engels (who acted as a second father to Tussy) and the diverse circle of radicals and political refugees who thronged the round reading room at the British Museum in the second half of the 19th century. Domestic and personal lives merge with the ferment of the age.

In her teens Eleanor became her father’s amanuensis, transcribing his notoriously illegible handwriting and generally organising his paperwork. Small wonder that she emerged into adulthood with all her father’s intellectual resources, and with an understanding of economic history and theory few could match. She was, to all intents and purposes, Marx’s creation. As Eleanor wrote, “I remember his once saying a thing that at the time I did not understand and that even sounded rather paradoxical. But I now know what he meant …My father was talking of my eldest sister and of me and said: ‘Jenny is most like me. But Tussy is me.’ ”

Eleanor was a more agitprop version of the bookish Karl. She led striking dock workers and gas workers, organising their emerging unions’ activities and joining their demonstrations. She ghosted any number of articles and manifestos for male union leaders and political activists. She addressed a crowd of 250,000 at the first May Day rally in London and toured the US, speaking out against the conditions of manual labourers.

Intellectually, what she brought of her own to the political arena was a vision that incorporated the rights of women. As she wrote in 1886 in The Woman Question, “For women, as for the labouring classes, no solution of the difficulties and problems that present themselves is really possible in the present condition of society.”

But Eleanor’s life, as Holmes shows, was tragically flawed around “the woman question”. At the moment she grasped and publicly articulated the connection between socialism and feminism, she became personally involved with a man who would fatally undermine her. Fellow socialist and playwright Edward Aveling was – in Eleanor’s friend George Bernard Shaw’s words – an “agreeable scoundrel …quite a pleasant fellow who would have gone to the stake for Socialism or Atheism, but with absolutely no conscience in his private life. He seduced every woman he met, and borrowed from every man.”

He and Eleanor were collaborators in their work for socialism, even for feminism. But beyond the endless workers’ rallies and union meetings, their relationship was disastrous from the start. Aveling brought Eleanor down in a way no policeman at a rally or debating adversary on a public stage could ever have done.

Thanks to Holmes’ fresh and vital style – not to mention her endearing partisanship – Eleanor Marx: A Life reads less like a biography than a 19th-century novel. Its close might indeed be modelled on Flaubert’s Madame Bovary, translated into English for the first time by Eleanor Marx in 1886.

Somewhere between March 27 and 31 1898, Eleanor learnt that the feckless, philandering Aveling had secretly married one of his actress amours. For 14 years Eleanor had accepted her own unconventional – and, to many, scandalous – cohabitation with Aveling as necessary, believing him to be already married. In fact, she discovered, his wife had died some years earlier. Eleanor had turned a blind eye to his affairs, his reckless spending, his many loans from her friends never repaid, his long absences and neglect. But this final betrayal was too much.

On March 31, she and Edward argued violently and he left her home in Sydenham, southeast London. Eleanor sent her maid Gerty to the pharmacist with a prescription for chloroform and prussic acid. Sent out on a further errand, Gerty returned to find the 43-year-old Eleanor motionless in bed. “Her long, dark hair was loose, her eyes fixed open,” writes Holmes. “Her face and body had changed colour, to a lurid mottled indigo. Gerty saw that Eleanor was wearing her favourite white muslin summer dress. It was unseasonal. She had washed, ironed and starched it herself, then laid it away in lavender and tissue paper for the winter.”

Thus the life of one of Britain’s most celebrated intellectuals and activists of the late 19th century came abruptly to an end, to be all but forgotten. Thankfully, however, Holmes has given back to us an unforgettable Eleanor Marx.

Lisa Jardine is professor of Renaissance Studies and director of the Centre for Humanities Interdisciplinary Research Projects at University College London