ANNE STEVENSON IS A well-kept secret. She has published 18 volumes of poetry, but you won't find her in The Nation's Favourite Poems. She has lived and written in Britain for more than 40 years but has never won a national poetry prize. She was a contemporary of Sylvia Plath and Ted Hughes but hasn't come within a mile of their fame.

All that might be about to change, however. If there is such a thing as a poetry jackpot, Stevenson has just hit it: this year she has won three important American literary prizes, together worth $260,000 (£130,000), and in 2008 the Library of America will publish a new edition of her Selected Poems, edited by Andrew Motion. All the more remarkable, this sudden rush of recognition has come in her 75th year.

Stevenson's creative powers are undiminished by age. Approaching her Victorian townhouse at the top of a steep hill in Durham, I hear her playing piano: a complex passage, fortissimo chords leaking into the street. Inside, I am struck by her birdlike alertness: sharp features framed by a schoolgirl fringe, direct, canny eyes. She has been deaf since her mid-thirties, but a cochlear implant allows her to hold close conversations, as long as she can see the other person. At times, struggling to hear, she leans forward, face creasing with concentration, eyes searching.

Why all these awards, I ask, and why now? Stevenson puts it down to her recent Poems 1955-2005, which had a good reception in America: “I think people were surprised because until then I had been known only as Sylvia Plath's biographer [Bitter Fame: A Life of Sylvia Plath was published in 1989], so they were really reading me as a poet for the first time. The poems in that collection form quite a body of work.”

Taken together, Stevenson's poems create a landscape that is, as the poet George Szirtes writes, “humane, intelligent and sane, composed of both natural and rational elements, and amply furnished with patches of wit and fury”. Her language is often direct, but her lines are taut with challenging ideas, and sprung with a tough survival mechanism; a willingness to bear one's cross, a need “To charm the world and not be crushed by it”.

She has always been wary of reputation — her manifesto poem Making Poetry describes the necessity of evading “the ego-hill, the misery-well,/the siren hiss of publish, success” — and although obviously pleased with her Indian summer, she maintains that prizes themselves do not interest her. “If your poems are good they win the ultimate prize of surviving you. That's why you keep your finger on the thread of Ariadne through the maze; if you're careful you can see it glistening ahead of you in the distance.”

Following the thread of Stevenson's own life — through four marriages, three children, and dozens of homes on both sides of the Atlantic — is not easy. She was born in Cambridge in 1933, the year that Hitler came to power; her American parents lived there while her father studied philosophy. Soon they moved back to the States, where Charles Stevenson taught at Yale until his book Ethics and Language earned him a sudden dismissal (its insistence on the moral relativity of language proved unpopular at a time when the Allies needed Hitler to be pure “evil”). They finally settled in Ann Arbor, Michigan.

Anne's mother fostered a love of fiction, her father a passion for music and poetry: by the time that she reached university, Anne had read all of Shakespeare and most major English novels, and was an accomplished pianist and cellist. Both Anne and her younger sister Diana were enthusiastic pupils: “She took violin lessons and fell in love with her violin teachers, one after the other, I took piano lessons and fell in love with my piano teachers — irrespective of sex.”

Anne studied cello for two years at the University of Michigan before deciding that she would never be a first-rate cellist. But she never abandoned music — it became the springboard and the backbone of her verse, “the sound leading the hand”, as she writes in Making Poetry.

Her engagement to a childhood friend, Robin Hitchchock, took her back to Cambridge in 1954, where she glimpsed the life of “real” poets. His mother, Helen, ran St Botolph's Rectory, a student lodgings and the “spiritual home” of Ted Hughes and his group, who named their magazine St Botolph's Review after it. When she stayed at St Botolph's Anne would hear the poets singing boisterously in the kitchen but never joined them: “I was too shy, and Robin would have been very disapproving.”

Had she met Hughes and Plath, her life might have gone in a different direction; instead she had a daughter and followed her husband, a management consultant, to London, Belfast, Georgia and Mississippi. “We were living in so many places that I never made any friends: I became very lonely. And I was not a very good mother. I lived in a period when women who had, throughout university, been the equals of men suddenly found themselves settled, with small children, without help, with no way to escape... Although I didn't go mad like Sylvia Plath, I got pretty close to it.”

Here the thread begins to tangle. Stevenson and Hitchcock divorced, and, daughter in tow, she returned to the US to study. In Cambridge, Massachusetts, she married a Sinologist, Mark Elvin, and returned to England, to the other Cambridge, “to try being a wife again”. They had two sons and moved to Glasgow, where Stevenson escaped for a taste of the artist's life that had previously been denied her, moving in with the poet Philip Hobsbaum and — while sharing her children with Mark — joining a vibrant community of writers.

In Glasgow, she finished a long poem, Correspondences, which dealt — from a distance — with her family's puritan background and the stiff inherited morality that was paralysing her with guilt and anxiety. “When I began Correspondences I was one miserable girl. But by the end of it I had grown up a few moral inches.”

There were spells in Oxford, Dundee, Hay-on-Wye and Sunderland, a third marriage in the early 1980s, then her fourth (and current) in 1987, to a lawyer, Peter Lucas. Soon after, her Plath biography thrust her into the spotlight: its signs of sympathy for Hughes enraged Plath supporters, particularly Al Alvarez, who dismissed it as “a minor poet's envy of a major poet”. But by then reputation had ceased to matter much to Stevenson. “The great thing is learning not to take oneself so seriously. Life is short — very short — and you're going to be dead a long time.”

These days, death is part of her life; she has survived many friends and lovers, some remembered in a long poem entitled A Lament for the Makers in her new collection, Stone Milk. Death is present throughout the book but never seems to inspire fear; Stevenson takes comfort from placing our stories in the context of the greater, geological story of the Earth. Through DNA and memory we are — even after death — part of the “whole chain of existence”: “floating, stretching between,/the mind's harmonic mappings,/frail as gossamer”.

It's a pragamatic, holistic philosophy, and one that, as far as she is concerned, renders mythology and religion reduntant; prizes and plaudits too. All Anne Stevenson needs now, in the twilight years of an extraordinary life, is the knowledge that she has been a functioning link in the chain: “I think I have achieved my potential; I've done what I can do. I couldn't have done differently, and I couldn't have done better.”

Stone Milk by Anne Stevenson
Bloodaxe, £7.95; 72pp

Poems 1955-2005 by Anne Stevenson
Bloodaxe, £12; 413pp

Read a poem by Anne Stevenson here

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