Close-up: Eliza Lumley

The former chorister has given Radiohead the cocktail-jazz treatment

It is not yet a matter of record whether, way back in 1992, Radiohead had any idea that they would go on to become the most important band of their generation, nor, increasingly, one of the most radically reinterpreted. Last year, a collection of Jamaican artists called Easy Star All-Stars gave a reggae lilt to the Oxford act's paeans to existential angst with Radiodread: A Tribute To OK Computer, while Mark Ronson turned their 1995 single "Just" into a slice of hyperactive funk. And now comes Eliza Lumley, a former choral singer, to give them, of all things, the cocktail-jazz treatment.

She Talks in Maths: Interpretations of Radiohead is a very Fortnum & Mason kind of record: rarefied, elegant and wrapped up in mink. Oddly, it works. Released online last autumn, it topped the iTunes jazz charts and has now secured a physical release. "Singing the words of Thom Yorke is like singing TS Eliot," says Lumley. "There is something about the quality of his songs that, even broken down to their barest essentials, still sound impossibly strong."

A well-bred 31-year-old with hot-chocolate eyes and cheekbones you could slice ham on, Lumley studied theology and philosophy at Cambridge University, and sang in its choir, before spending much of her twenties acting on stage – Mamma Mia in London's West End, Tom Stoppard's Jumpers on Broadway – but felt inexorably drawn back to song. "I've done versions of Coldplay and Echo & the Bunnymen as well," she says, "but it was Radiohead that lent themselves most naturally to the form.

"I've decided to do the Smiths next," she reveals. "I wonder what Morrissey would think. He's quite the diva, isn't he?"

'She Talks in Maths: Interpretations of Radiohead' (£10.99) is out now on Archangel