Before I meet the formidable feminist, academic and critic Jacqueline Rose, she e-mails her mantra for 21st-century feminism:

"We are feminist. We fight injustice against women. We are not innocent. We are not in flight from the darkest secrets of the soul. For that reason, we do not need to subdue the world to our will in order to enact them. We are feminists. Listen carefully to what we have to say."

It is, of course, impossible not to listen carefully to what Professor Rose has to say in her thought-provoking, rigorously argued writing on feminism, literature and psychoanalysis. In Europe she is hailed as a public intellectual - she is also acknowledged internationally. Here, however, she remains "the thinking woman's thinking woman" since we do not celebrate intellectuals, especially intellectual women, as they do in, say, France.

Born in 1949 and educated at St Hilda's College, Oxford, where she read English, Rose is indubitably an intellectual of clout. She is the author of a dozen works of non-fiction, including the controversial The Haunting Of Sylvia Plath (1991), which led to a furious response from Plath's husband Ted Hughes over Rose's interpretation of some of the poetry - he thought she was calling his dead wife a lesbian.

In 2005, even more contentiously, Rose put Israel on the couch in her remarkable book, The Question Of Zion, which led to a torrent of hatred for daring to psychoanalyse the country. She has published books about Jacques Lacan, Peter Pan, Melanie Klein, and Proust and the Dreyfus case. In 2001 she wrote her only novel, Albertine, in which she sets out to restore the intelligence of Proust's beloved fugitive.

Now, she has written her 13th work of non-fiction, Women In Dark Times, a series of biographies of intellectuals and artists as diverse as the Polish Jew and revolutionary socialist Rosa Luxemburg, the glorious Marilyn Monroe and German-Jewish painter Charlotte Salomon, three women who have taught Rose "to think differently".

In 1919, Luxemburg was murdered by government henchmen; Monroe was possibly murdered in 1962; and Salomon died, five months pregnant, in Auschwitz. Three apparently tragic lives, yet Rose argues we must not see these women as victims, martyrs or, indeed, angels.

In addition, the London-based Professor of English at Queen Mary University of London, who takes up the Chair in Gender Studies at Cambridge University this month, honours the lives of Shafilea Ahmed, Heshu Yones and Fadime Sahindal, victims of so-called "honour" killings.

She concludes her book with an examination of three contemporary artists - Esther Shalev-Gerz, Yael Bartana and Therese Oulton - whose work "turns the world inside out".

These women, she asserts, are the heirs to Luxemburg, Monroe and Salomon. It is a breathtaking book and a challenging read - ambitious, scholarly and innovative, shedding dazzling light on Freud's "dark continent" of women.

So an interview with Rose is a daunting prospect, although she turns out to be warm and friendly - and funny, despite the seriousness of her work. We meet in a cafe in the heart of liberal, artistic, literary Hampstead, near Rose's home, which she shares with her psychoanalyst partner, Jonathan Sklar, and her daughter Mia, 20, whom she and her then partner, psychoanalyst and writer Adam Phillips, adopted as a baby from China.

I begin by asking her to unpack that mantra for me and she responds fluently. "It has seemed to me important for a very long time - and this goes back to my work on Sylvia Plath - that feminism says what is unjust and cruel about the world and unequal about it, but that it does not fall into the trap of therefore presenting women as all nice, innocent or virtuous.

"Also, I think the rhetoric of innocence is a deadly rhetoric, because if you think of yourself as a pure, innocent subject who can do no wrong, then for some reason you are justified in doing wrong to others, whom you can then classify as bad or evil. I think when that becomes a gender division, it is particularly troubling. More importantly, though, that mantra is really an extension of what has been one of feminism's most basic propositions, that the personal is political. My idea is I am suggesting we have not quite plumbed the depths of what it means to say the personal is political.

"I also think some (feminists) tend to run a bit scared when the personal starts to touch on the complexities of our inner lives, because it slightly spoils the story."

You can turn this around, though, by saying the political is the personal?

"Yes, you can!" she says."And that leads to the second point, the idea that when you get into the murky depths of the personal, then feminism should back off. I think feminism should see it as its gift to the world to point out (everything) those most murky aspects of personal life are offering to them either violently or creatively. What is important about Luxemburg, Monroe and Salomon is they are so in touch with something intractable and difficult about their personal lives that it feeds into them and allows them insights to see things that otherwise, I think, they would not see."

She loves how Monroe retaliated to Arthur Miller's dedication of The Misfits to Clark Gable as "a man who does not know how to hate," by saying, "I think every human being knows how to hate, because if they don't know how to hate, they wouldn't know how to love or any of the in-betweens."

Monroe, she points out, wrote in her journal: "I am violent. I know I am violent." Rose believes: "She had no interest in presenting herself as an innocent flake. And, of course, the culture idealised her as a kind of perfection and purity, a sexual innocence that was always available. The subtext of that is she has no mind. When you say that somebody has no mind - a dumb blonde - you are actually denying them the right not just to intelligence but psychic complexity. I think that, despite the biographies and other studies, no one has ever politicised her before as I do in this book."

So how do her three heroines connect? Each of these women was a truth-teller, replies Rose, straddling the divide between the political and the unruliness of their inner lives. "At first glance they could not appear more different: the bold revolutionary, the painter hidden from the world, the film icon. In fact, they are profoundly linked, they are historical sisters - they carved out an arc that stretches from one woman to the next across some of the most dramatic moments of the last century - revolution, Nazism, the American dream. Each fought 'dark with dark'."

Working on the book took her into some dark places as she pursued her researches into our times, following another vital strand of modern feminism, "making visible the invisible histories of women" in her powerful chapters on honour killing - "a way of reminding us of the worst that a still patriarchal world is capable of. We live in a testosterone-led culture. Since I wrote about those killings, it is getting worse."

Rose begins and ends her book with a clarion cry for "a scandalous feminism, one which embraces without inhibition the most painful, outrageous aspects of the human heart, giving them their place at the very core of the world that feminism wants to create... The feminism I am calling for would have the courage of its contradictions."

The future of feminism, she believes, depends on how we, as women, choose to talk about each other, and her next public lecture and possibly her 14th book will be an exploration of violence against women. "It's a very scary time for women - hatred has really come to the surface."

She pauses and says crisply: "Women have been reasonable for far too long."

Women In Dark Times by Jacqueline Rose is published by Bloomsbury, £20