Weaving together the stories of a teenage girl in modern-day Cambridge and a 15th-century Italian artist, Ali Smith’s How to Be Both has won the Baileys women’s prize for fiction, with chair of judges Shami Chakrabarti describing it as a work that will still be read in 100 years.

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Already the winner of prizes including the Costa novel award and the Goldsmiths, and shortlisted for the Man Booker, Smith’s novel beat a strong shortlist to win the £30,000 award on Wednesday evening. Intended to celebrate “excellence, originality and accessibility in women’s writing from throughout the world”, the Baileys prize, formerly known as the Orange, has been won in the past by Lionel Shriver for We Need to Talk About Kevin, and Zadie Smith for On Beauty.

“I think she is a literary genius,” said Chakrabarti, director of the civil rights group Liberty. “I haven’t felt that way about reading since I was doing my English A-levels. It reminded me of what it felt like reading Virginia Woolf, James Joyce, all of the greats … that this is not a good book, this is a great book, and people are going to be reading it long after I’m dead.”

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How to Be Both is a split narrative, and half of its copies were printed with the story of the teenage girl, George, whose mother has recently died, first. The other copies begin with the story of Francesco del Cossa, an artist in 15th-century Ferrara who in Smith’s story is born a girl but raised as a man.

In a statement, Chakrabarti called How to Be Both a “tender, brilliant and witty novel of grief, love, sexuality and shape-shifting identity”. She added: “The way she has the ancient and the modern, the high art and the references to classical art, but also the contemporary nature of the story, and the universal themes of grief, loss and gender … it’s all so effortless … there’s also really contemporary stuff like pornography, technology and surveillance.”

Chakrabarti said she had read How to Be Both both ways – with George’s perspective first, and then with Francesco’s. “I think if I were advising somebody, and this is probably deeply controversial and Ali and her publisher will probably be very cross with me, I think the best way in is to read the modern story first. But others would disagree.”

This year’s Baileys judging panel also included Laura Bates, founder of the Everyday Sexism Project, the columnist Grace Dent, the novelist and winner of the inaugural Orange prize in 1996 Helen Dunmore, and Channel 4 news presenter Cathy Newman.

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Chakrabarti said the panel “went round the houses” to choose Smith as their eventual winner from a shortlist that also included Sarah Waters’ The Paying Guests – the bookies’ favourite – Rachel Cusk’s Outline, Anne Tyler’s A Spool of Blue Thread, Kamila Shamsie’s A God in Every Stone and Laline Paull’s debut The Bees.

“It wasn’t easy,” she said. “But in the end How To Be Both was a very popular choice.”

Smith, who was born in Inverness, is the author of four collections of short stories and six novels, including the Booker and Orange-shortlisted Hotel World, and the Whitbread prize-winning The Accidental. She is critically acclaimed, but Chakrabarti hoped that the Baileys win would bring her work to a wider audience. “In my heart I believe she will be read in 100 years’ time, but I want her to be really broadly read now,” she said.

The women’s prize for fiction was set up after researchers led by the novelist Kate Mosse found that by 1992, only 10% of novelists shortlisted for the Booker had been women. In 1991, not a single female author was shortlisted for the prize. The award has been described as “sexist” by the novelist AS Byatt, who said that it “assumes there is a feminine subject matter – which I don’t believe in”. But Chakrabarti called new research from the novelist Nicola Griffith, which found that a novel is more likely to win a literary award if it is about a man, “vindication of the role of the prize”.

Looking at the subject matter of the winners of six major literary awards, including the Booker and the Pulitzer, Griffith found the majority, even if written by women, were told from the point of view of men or boys. None of the 15 Pulitzer winners was told wholly from a female perspective, she wrote, while between 2000 and 2014 the Booker has been won by nine books by men about men, three by women about men, two by women about women, and one by a woman about both.

“Certainly the results argue for women’s perspectives being considered uninteresting or unworthy. Women seem to have literary cooties,” Griffith has written.

“Women’s stories and their characters are not being celebrated enough in modern publishing,” agreed Chakrabarti. “Women are great readers as well as great writers and understandably they want their stories to be told.” Gender injustice, she added, is still the “greatest injustice on the planet”.

“There’s a lot of work to be done, and a lot of stories to be told, and stories are what I believe change the world more than anything,” she said.

How to be both by Ali Smith (Penguin, £8.99). To order a copy for £6.99, go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.