It is nearly 50 years since Instead of a Letter, Athill's memoir of betrayed love, her "failure" as an unmarried, childless woman, and her building of a triumphantly different kind of life. Since then, and since retiring from André Deutsch, where she was one of the most respected editors of her generation, she has become a literary celebrity, winning the Costa Biography award in 2008 for her bestselling reflections on ageing, Somewhere Towards the End. With cool intelligence she has studied from first principles the rules of loving, living, dying; she has reasoned aloud in ways which might help us make our own decisions.

This new book is a collection of letters: Athill's side of a 30-year correspondence with her friend, the neo-pop poet Edward Field in New York, spanning the 1980s and 1990s and stopping just short of Athill's 90th birthday in 2007. They cover her sad last years at André Deutsch ("The House of Usher Incarnate"), the death of her mother, the writing of Stet (how candid can she be about Deutsch himself?), and her new existence as a celebrated writer. These are vivid reports on life in late 20th-century Britain as experienced by a writer, editor, daughter, partner and pensioner with an extraordinarily "beady eye" on human relations and a phenomenal capacity for making the most of everything that comes her way.

When Field first got in touch (about the work of Alfred Chester), he thought he was writing to "a typical English spinster out of a Barbara Pym novel". The first meeting put him right, and an unlikely transatlantic friendship formed. Friendship, in fact, is the enduring subject of this book, as sex has been the subject of previous books. Other topics come and go, but the pleasure of affection runs through all the letters. Athill was not expecting to make new friends in her 70s, just as she was not expecting a new lover at 60. On both counts she has proved herself encouragingly wrong.

The relationship between Athill and Field is a compelling one. Determined to write unflinchingly about their lives, they are conspirators in their quest for honesty. There is a memorable image of Athill sitting in one of the "fat-farms" she (very honestly) tells us that she visits, surrounded by "the most tinkling-tea-spoons kind of small talk" while reading Field's "poems about shitting". She feels she can tell him anything; his openness encourages hers.

But they have different sensibilities and limits, which Athill probes with acuity: "I guess it is one of my deepest instincts to control by being beady-eyed; while you have this wonderful strong instinct to feel  to risk yourself on the flood of feelings." Athill knows that she would not survive an encounter group meeting, for example, and she advises Field against hypochondriacal poetry: "I think there's an automatic flinch from Being Sorry For Yourself in most Brits." Very true, and it is partly the resilient cheerfulness of Athill's writing that has appealed to British readers.

There is a Jamesian fascination in the Englishwoman writing to the New Yorker, and the cultural differences produce some good social comedy. In his introduction Field emphasises the spartan decor of Athill's flat with its inadequate gas fire. "Nonsense, it was a very superior and efficient gas fire," chips in Athill in editorial square brackets, glad to confirm Field's sense of her as "a sturdy daughter of the famously damp isles of Britain".

But their discussions go well beyond attitudes to heating, telling though these are. Both are carers for their partners, negotiating the painful territory of illness, obligation and dependence. Long-term care is a subject sorely lacking in adequate literature, and (as she has already done for old age) Athill opens the way for more truthful discussion.

Field's partner Neil Derrick is blind, and needs increasing levels of support. Athill is awed by their capacity as a couple to get on with things, "divesting the situation of anything unusual or poignant". For her part, she finds herself in the role of carer, first for her mother in Norfolk, and then for her partner, the Jamaican playwright Barry Reckford. Athill has reflected on both relationships before, but here we find her letting out frustrations without the calming influence of hindsight and voicing her ongoing internal debate. The question is largely about loyalty. To her mother, she owes "the consolation" of a daughter's care. She gives it, and knows she is loved for it. With Barry it is more complicated. They were lovers, but stopped being lovers. They lived together, but without the agreed commitments of marriage. What, then, do they owe each other?

Athill wrote in Somewhere Towards the End about her suspicion of relationships which bind people together beyond the fading of love. Her own parents' marriage had taught her the dangers. "Loyalty is not a favourite virtue of mine," she wrote. "When spouses are concerned, it seems to me that kindness and consideration should be the key words, not loyalty." As Barry turns away from her to watch the television blankly, is it her duty to accept the "thralldom" of his dependency, or is it important (for herself, for others) that she resist it? She is characteristically frank about the hospital visits and exhaustion, working out what she is learning and what she is loathing.

Athill tackles the big questions through small increments. Her subject is daily life, which means that letters are an ideal vehicle. She does spirited sketches of OAP life: left and right eye disagree with each other; hearing aids are compared. When two teeth crack she considers a course of Prozac, but plumps for a rereading of Trollope instead. "I'm so busy being retired," she says, dashing from life-drawing to chair-caning and back to dog-sitting (yes, the dog is getting old as well). Her stories about driving would be less encouraging if you happened to be coming in the other direction, but she hangs on to her licence (even her trips to the magistrates' court are jolly) and buys a new car. She undertakes epic journeys in search of typewriter ribbon ("one might as well be seeking a blacksmith"), before eventually capitulating to the computer. Email sceptics who mourn the end of letter writing may be heartened to find no discernible diminishment in Athill's expressive powers.

Her energy for travel and new people is unabating, whether she's falling in love with a burgomeister in Hungary or feeling in Dominica a clarity of perception she has not felt since youth. She does not have much time for Virginia Woolf, but she describes here what Woolf might call "moments of being" and bears witness to the fact that such moments can be as powerful at 90 as at 19.

Does Field, I wonder, feel the same? This is only half of a correspondence, but the reason for the lopsidedness is also part of the reason these letters are so fascinating. While Field was carefully filing Athill's letters in a concertina file, Athill was reading his with delight and throwing them away  as she had thrown away Jean Rhys's letters, and doubtless many other documents which would otherwise be destined for climate-controlled reading rooms. "How I have kicked myself," she says, but there is something exhilarating in the sense of life going on without posterity impinging. "Letters are fixed in my mind as being talking, and thus ephemeral," she explains, and it is easy to believe. Fluent, confiding, dawdling for a bit, then speeding into an anecdote, these letters allow us to eavesdrop on a conversation which is all the more seductive because Athill did not expect anyone else to be listening.

We're still listening (but not too comfortably: Athill is no comfort-merchant in a rocking chair), when Athill abruptly writes FINIS. She observes here, as she observed in Somewhere Towards the End, that in old age it is impossible to end with a bang. (The repetition from one book to the next suggests part of the problem.) "We have become old," she writes, and "the detailed swapping of symptoms does undeniably become boring." This feels for a moment like an abrogation of her duty as the nation's appointed writer on ageing to tackle the really boring bits that no one else has touched. But what am I thinking? She owes us nothing. She has given a very great deal.

Alexandra Harris's Virginia Woolf is published by Thames & Hudson.