Madeline Miller’s 2011 retelling of the Iliad, The Song of Achilles, recast the epic as a love story between Achilles and Patroclus, taking us into the emotional heart of some of the most moving and memorable passages in the poem. The book was a surprise hit, winning Miller – then a Latin and Greek teacher – the Orange prizecorrect and a place on the bestseller lists. What she was doing was nothing new – writers have been reimagining Homer’s work since the Aeneid – but the contemporary tone and modern sensibility did something extraordinary to the well-known tale. The best historical fiction balances the past and present in the text, so that it both celebrates and collapses the distance between then and now. In The Song of Achilles, Miller rendered that ancient war thrillingly, grippingly present; her vision of the relationship between Achilles and Patroclus was one of steaming, timeless sensuality.

Miller begins Circe in the court of Helios: the sun god and her heroine’s father. “His palace was a neighbour to Oceanos’, buried in the earth’s rock, and its walls were made of obsidian.” From the start, we are made aware of Circe’s inferior status – “Circe is dull as a rock,” says her father. She is named after her yellow eyes – circe means hawk – and for the “thin sound” of her crying, which we later learn is because she has been born with the voice of a mortal, not a god. Circe witnesses the punishment of Prometheus and this kindles a deep sympathetic interest in humans. Soon after, she meets Glaucos, a fisherman, and they become lovers. Wishing to keep him from his own mortality, she makes the first use of pharmaka – the magical herbs that activate her sorcery. Glaucos becomes a god, “towering like a sea-surge”, green-haired and trident-wielding. He swiftly grows tired of the unprepossessing Circe and transfers his attentions to Scylla, a beautiful sea-nymph. Circe, enraged, turns her witchcraft upon the nymph, and is exiled to a beautiful, unpeopled island.

It is here, on Aiaia, that Odysseus finds her, happily surrounded by tame wolves and lions and swine – the latter are earlier visitors that she has bewitched after an unwise sea captain attempts to rape her. As with her previous novel, the great skill here is the way Miller gives voice to a previously muted perspective in the classics, forging a great romance from the scraps left to us by the ancients. If The Song of Achilles recovered a half-buried homosexual love story from the Iliad, Circe gives us a feminist slant on the Odyssey. “Humbling women seems to be a chief pastime of poets,” Circe says at one point. “As if there can be no story unless we crawl and weep.” It’s fitting that Circe is published just a year after the first major female translation of the Odyssey, by Emily Wilson. Wilson said in her introduction to that translation “the question of who matters is actually central to what the text is about”.

In Miller’s vision Circe, who is passed over in a few dozen lines in the Greek original, matters deeply. Hilary Mantel has spoken repeatedly of the problems that arise when modern ethical mores are placed in the mouths of historical figures. In her Reith Lectures, she says: “This is a persistent difficulty for women writers, who want to write about women in the past, but can’t resist retrospectively empowering them.” Miller flouts Mantel’s interdiction winningly, joyously, and in a way that is powerfully affecting.

The Song of Achilles may have been a bestseller, but its critical reception was decidedly mixed. Fusty – and almost always male – critics lamented the historical inaccuracies, the liberties taken with the text, the cliches. They missed the point that Miller was seeking to popularise stories that were first popular three millennia ago, employing the tools of the novelist to reveal new internal landscapes in these familiar tales. In her Circe, Miller has made a collage out of a variety of source materials – from Ovid to Homer to another lost epic, the Telegony – but the guiding instinct here is to re-present the classics from the perspective of the women involved in them, and to do so in a way that makes these age-old texts thrum with contemporary relevance. If you read this book expecting a masterpiece to rival the originals, you’ll be disappointed; Circe is, instead, a romp, an airy delight, a novel to be gobbled greedily in a single sitting.

• Circe by Madeline Miller is published by Bloomsbury (£16.99). To order a copy for £12.99 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99