'I am becoming more radical with age," says Nawal El Saadawi, laughing. "I have noticed that writers, when they are old, become milder. But for me it is the opposite. Age makes me more angry."

This is a startling admission. It is hard to imagine how El Saadawi – the Egyptian writer, activist and one of the leading feminists of her generation – could become more radical. Wearing an open denim shirt, with her hair pulled into two plaits, she looks like the rebel she has always been. It is only the pure white hair, and the lines that spread across her face as she smiles, that give away the fact that she is 79. She has, she tells me, "decided not to die young but to live as much as I can".

El Saadawi already seems to have lived more lives than most. She trained as a doctor, then worked as a psychiatrist and university lecturer, and has published almost 50 novels, plays and collections of short stories. Her work, which tackles the problems women face in Egypt and across the world, has always attracted outrage, but she never seems to have balked at this; she has continued to address controversial issues such as prostitution, domestic violence and religious fundamentalism in her writing.

This has come at considerable cost. In 1972, her non-fiction book Women and Sex (which included criticism of female genital mutilation) led to her losing her job as director general of public health for the Egyptian ministry of health. In 1981, her outspoken political views led to her being charged with crimes against the state and jailed for three months – she used the time to write Memoirs From The Women's Prison on a roll of toilet paper, with an eyebrow pencil smuggled in by a fellow prisoner. In 1993 she fled to the US after death threats were issued against her by religious groups.

Her work continues to be explosive. Her play, God Resigns in the Summit Meeting – in which God is questioned by Jewish, Muslim and Christian prophets and finally quits – proved so controversial that, she says, her Arabic publishers destroyed it under police duress. And recently her criticism of religion, primarily on the basis that it oppresses women, has prompted a flurry of court cases, including unsuccessful legal attempts both to strip her of her nationality and to forcibly dissolve her marriage.

As El Saadawi prepares to talk about her life at a PEN literary festival on Friday, she is unrepentant. "It's all worth it," she assures me. "If I went back I would do it all again. That is what I have learned from my experiences, that I was on the right track." Her energy, she insists, comes from the 10 to 15 letters she receives every day from people who say their lives have been changed by her writing. "A young man came to me in Cairo with his new bride. He said, I want to introduce my wife to you and thank you. Your books have made me a better man. Because of them I wanted to marry not a slave, but a free woman."

El Saadawi is "a novelist first, a novelist second, a novelist third", she says, but it is feminism that unites her work. "For me feminism includes everything," she says. "It is social justice, political justice, sexual justice . . . It is the link between medicine, literature, politics, economics, psychology and history. Feminism is all that. You cannot understand the oppression of women without this."

She says she has been a feminist "since I was a child. I was swimming against the tide all my life." Her eight brothers and sisters "were totally different. Some of my sisters are now veiled and they think I am very, very radical. They love me, and we see each other, but we don't visit much."

In her first autobiography, A Daughter of Isis, she recalls her outrage when she began to realise daughters were not considered equal to sons. When her grandmother told her, "a boy is worth 15 girls at least . . . Girls are a blight," she stamped her foot in fury.

In that same book she writes about the horror of female circumcision. "When I was six, the daya (midwife) came along holding a razor, pulled out my clitoris from between my thighs and cut it off. She said it was the will of God and she had done his will . . . I lay in a pool of blood. After a few days the bleeding stopped . . . But the pain was there like an abscess deep in my flesh . . . I did not know what other parts in my body there were that might need to be cut off in the same way." Later, while working as a doctor, she saw for herself the terrible physical damage female genital mutilation could cause; she campaigned for 50 years, she says, for it to be banned in Egypt. A ban was finally instituted in 2008, but she says the practice "still happens – it is even increasing. Some religious leaders talk against it, but others are for it."

Circumcision wasn't the only horror El Saadawi faced as a child. Brought up in a middle-class Egyptian household, she was expected to become a child bride, but refused; she blackened her teeth and dropped coffee over one would-be suitor who came to call. "When I was a child it was normal that girls in my village would marry at 10 or 11," she says. "Now, of course, the government is standing against that because it is unhealthy. And it happens much less. But we are having a relapse again, because of poverty and religious fundamentalism."

El Saadawi's desire to study was so great that her parents were eventually convinced she would benefit from university. She believes that her radical views were formed, at least in part, by training as a doctor. "When I dissected the body it opened my eyes," she says. "Also, I think I have the gene of my grandmother who was a rebel. My sisters and brothers took another gene."

At medical school she fell in love with a fellow student, Ahmed Helmi, who was engaged in the fight against the British occupation of the Suez. They married and had a daughter – but divorced when he came back from the fighting embittered and turned to drugs. She later married a lawyer, who "said to me you have to choose between me and your writing. I said my writing." In her second volume of autobiography, Walking Through Fire, she describes how he refused to grant her a divorce, announcing that, "It is the man who decides to divorce and not the woman"; in desperation, she threatened him with her scalpel. For the last 45 years she has been married to the novelist, doctor, and former long-term political prisoner, Sherif Hetata, with whom she had her second child, a son.

El Saadawi's daughter, Mona Helmi, has followed in her footsteps, becoming a writer and poet. In 2007, Mona became the target of controversy when "she wrote a beautiful article on Mother's Day," says El Saadawi. "She asked, 'What present can I give to my mother – shall I give her shoes? A dress? The gift I will give is to carry her name.'" The article was signed Mona Nawal Helmi. "They took her to court – they said it was heresy because in the Qur'an women should take the name of the father not the mother."

Although Mona won the case, El Sadaawi says that this, and another court case in 2002 – brought by a lawyer who sought to have El Sadaawi forcibly divorced on the basis of apostasy (abandonment of religion) – has left her bruised. "I feel I am betrayed by my country. I should be awarded the highest prize in Egypt for what I have done regarding injustices against women and children, and for my creative work." But she says her writing has given her an alternative sense of identity. "Home to me is the world because my books have been translated into more than 30 languages. People feel they know me and the minute they talk about my life or books I feel at home. Home is where you are appreciated, safe and protected, creative, and where you are loved – not where you are put in prison."

She still refuses to tone down her work. "I am very critical of all religions," she says. "We, as women, are oppressed by all these religions." It is religious extremism, she believes, that is the biggest threat to women's liberation today. "There is a backlash against feminism all over the world today because of the revival of religions," she says. "We have had a global and religious fundamentalist movement." She fears that the rise of religion is holding back progress regarding issues such as female circumcision, especially in Egypt.

In a bid to address this, she has helped to found the Egyptian chapter of the Global Solidarity for Secular society. She believes religion should be a personal matter, and approves of France's ban on all religious symbols, including the hijab. "Education should be totally secular. I am not telling people not to believe in God, but it should be a personal matter which should be done at home."

Despite the fact that her sisters wear the veil, she refuses to accept it as a free choice. "What do we mean by choice? It is pressure, but it is hidden pressure – she is not aware of it. I was exposed to different pressures from my sisters. We are all the products of our economic, social and political life and our education. Young people today are living in the era of the fundamentalist groups."

El Saadawi says that she is dismayed by the relaxed attitude of young women who do not realise what previous generations of feminists have fought for. "Young people are afraid of the price of being free. I tell them, don't be, it is better than being oppressed, than being a slave. It's all worth it. I am free."

And, she adds, there are more battles for her on the horizon. "A new university opened in Egypt and I was asked to teach, but the top people said no. They are afraid. So that is the next thing. I will work towards teaching in Egypt." A fighter to the last.