Sex and gender have become an issue in the general election, making Susanna Rustin’s measured and insightful book, Sexed: A History of British Feminism, even more timely. Kemi Badenoch, the women and equalities minister, has promised that Conservatives will strengthen existing rights to single-sex spaces, for instance in prisons and refuges, so they can only be accessed by biological women. She defends the philosophical belief that “biological sex is real, important, immutable and not to be conflated with gender identity”, a view already legally protected in the UK.

Labour has committed vaguely to “modernise, simplify and reform” the 2004 Gender Recognition Act after the ditching of an initial promise to allow a man or a woman to self-identify their gender, removing the requirement for medical evidence and irrespective of the genitalia they possess (and avoid questions such as “Can a woman have a penis?”).

Rustin’s view is that sex-based rights “are fundamental to feminism” and she rejects the notion that this is transphobic. Defence of these rights, she argues, has fuelled a decade-long grassroots revival of the women’s movement, marked by high-profile cases of “gender-critical” women sacked for their beliefs and then successfully taking their employers to employment tribunals. These include Maya Forstater, whose landmark case meant that discrimination against holders of gender-critical views became illegal three years ago.

That hasn’t stopped a “bitterly contested” hostile “debate” marked by insults, false accusations, lack of clarity, trashed reputations, lost careers, cancelled events and juggling with pronouns (he, she, they, them) in an increasingly gender-fluid society. Those who seek to defend sex as a protected characteristic part of the 2010 Equality Act – rejecting, for example, “people” who menstruate and chest-feed babies – have been labelled Terfs, trans-exclusionary radical feminists.

Rustin argues that there are practical reasons to acknowledge biology, for instance in addressing female cancers, birth control, fertility and maternity practices, as well as male violence against women and girls. However, some trans activists, their supporters and academics, such as the influential Judith Butler and Amia Srinivasan, argue that sex “is itself already gender in disguise”.

We are who we choose to be, in other words – even if that means a convicted male sex offender, self-identifying as a woman, has the right to be in a women’s prison. Gender-critical feminists such as Rustin – rightly in my opinion – argue that as long as the patriarchy flourishes, then biological women have the right to protection from its worst excesses.

What Rustin attempts to address in Sexed is the question of why and how the present-day feminist focus has apparently narrowed so tightly on sex and gender when so many inequalities still flourish. She provides a brisk, selective hurtle through 230 years of feminism, beginning in 1792 with Mary Wollstonecraft’s A Vindication of the Rights of Women, travelling through the foundations of feminist economics such as the arrival of the family allowance and defrosting the notion of “natural” female frigidity, ending with today’s sex-based rights movement of which Rustin is a part.

Feminism, past and present, is a messy, chaotic, contradictory business but she attempts to impose some order by dividing her book into chapters headed things like rebels, organisers, crusaders, suffragists, legislators, housewives (how the postwar years became the most socially progressive and least feminist; the Beveridge welfare state, “a man’s plan for men”).

A theme of the book is the paradox at the heart of feminism. Women have traditionally been treated as “other” than men, inferior in mind and body, better suited to “the uncompetitive activity of… home”, as Freud bizarrely put it. Females are allegedly captive, for ever constrained by their biology; biology that older women and, less so, younger women now fiercely espouse. In trying to shed the conditioning of these man-made versions of femininity and gain equality, Rustin argues, the differences between biological men and women that constitute “sex” as opposed to gender, a social construct, have been erased over the years. In 1932, Winifred Holtby became one of the first feminist writers to posit substituting the word “sex” with “gender” on the grounds that the former was too weighted with the kinds of biological connotation that dragged women down.

Reading Sexed, even a war-weary veteran of several waves of women’s liberation will find something fresh, while those exploring the issues for the first time have to be impressed by these pioneers, middle-class and working-class, elbowing their way into previously male-only spaces.

Barbara Bodichon, for example, co-founded Girton College, Cambridge and established the English Woman’s Journal in the 1850s, which carried articles on poverty, factory conditions, sex work and politics; anything but domesticity.

Josephine Butler led the campaign to repeal the Contagious Diseases Acts, passed in the 1860s, which mandated the compulsory genital inspection of sex workers (but not their clients). As Rustin points out, Butler’s crusade was crucial because it was at a time when the British women’s movement advocated radical direct-action tactics, later influencing the suffragettes and demonstrating that well-behaved women don’t make history.

Feminism has always been about more than individuals, however charismatic. Division and dispute is a permanent part of the dynamic of women trying to break free – radical separatists pulling the more conservative elements to go further and faster, demand more.

Rustin, a leader writer on social affairs at the Guardian, ends by saying she is certain “there is an accommodation to be found between feminists (and gay and lesbian women) who want their sex-based rights to be upheld and transgender people who want their gender identities to be respected”. How it’s achieved she leaves for others to ponder.

“It is difficult to feel optimistic about the prospects for women and girls at the moment,” she writes. Yet Sexed is a powerful reminder of just how much women have achieved, fuelled by a sense of injustice, against the odds and relatively speedily. That’s why, in the women’s movement, pessimism has rarely had a place.

• Sexed: A History of British Feminism by Susanna Rustin is published by Polity (£20). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply