Diana Athill had lots of confidence. She understood the social class she came from and could stand outside it, looking in, whenever she chose. As she wrote in Stet, her memoir of her years in the publishing trade, she was a member of a caste: “one of the London-dwelling, university-educated, upper-middle-class English people who took over publishing towards the end of the 19th century from the booksellers who used to run it”. But she was also a white woman who had several black lovers in an age when that kind of relationship could be seen as a political statement; and she despised the “self-consciously beautiful writing” of the “quintessentially caste writer” Virginia Woolf. To her, “caste standards – it ought not to need saying – have no right to be considered sacrosanct”.

Her confidence helped her to be a writer, of course – it stands somewhere between “talent” and “connection” in the list of useful attributes – but it made her a fine editor, too. She was clear in her judgments and certain in her encouragement. We first met in the early 1980s, when a book I was allegedly writing for her publishing firm, André Deutsch, had long passed its delivery date. I took the work-in-no-progress to the office, where Diana read some of the first chapter aloud with such elegant enunciation that I was almost (though not quite) persuaded to carry on with the rest. At that time I didn’t know she’d been a writer, but then I read her two books of memoir, Instead of a Letter and After a Funeral, and was struck, as many others have been, by her frankness and clarity and the wonderful rhythm of her prose.

Then our roles changed. At Granta, I was the editor and she was the writer. Via a mutual acquaintance, she sent in a piece for the magazine about her professional friendship with Jean Rhys. I didn’t think the piece was our kind of thing – I was a wrong about this – but she mentioned it had been taken from a book she was writing. I asked to see the whole typescript of the book, which turned out to be Stet. She was 82 and about to embark on her Indian summer as a writer. Several other books and a magazine piece or two followed, and we republished her backlist. Very little editing was ever required. I can truthfully say that I could begin reading at any point on one of her typed pages and never want to stop, impelled through sentence after sentence by the delightful force of her narration, as though she was speaking to me.

Very occasionally, I suggested a change. There was too much sex, I thought, at the beginning of what turned out to be her most successful book, Somewhere Towards the End. That seemed an odd thing to say to a writer who was then close to 90, but I thought we didn’t need as many pages to establish the author’s pleasure in sex as a mechanical rather than psychological or emotional activity; an activity that in any case had left Diana behind. Diana agreed and the book was adjusted. My second suggestion had more interesting results.

I wondered to Diana if, towards the book’s close, her tone sounded too complacent. “Let me have a think,” she said, and soon after submitted a new passage that began: “Not long ago a friend said to me that I ought to be careful not to sound complacent, ‘because’ he added kindly, ‘you are not’.” She disagreed with her anonymous friend (I guessed it was me). She declared she was complacent. She had started out, she wrote, “wrapped warmly in my family’s belief that we were the best kind of people short of saintliness: a belief common in the upper levels of the English middle class and confirmed by pride in being English”. And though that “tribal smugness” and “wicked nonsense” had been smashed when her first and most important lover jilted her, self-satisfaction of another kind had returned with her late success. If this was smugness, and she couldn’t help feeling that it was, then she had to report that “though repulsive to witness, it is a far more comfortable state to be in than its opposite”.

So she was happy to be smug – you might say smug about it – because comfort was what one needed on the “downhill journey” of advanced old age. Disguised in her attractive and thoughtful sentences, there was sometimes the brisk approach of a governess who wants to settle her brood’s every question by being sensible. What was sex? What was death? What was the point of moping after the first or fearing the second? She knew her nature – she confessed to a “nub of coldness” at her centre – but it still gave me a jolt when in conversation she might scoff (“Ridiculous!”) at the memory of a dying old man crying with fear in his hospital bed or other evidence of irrational human behaviour. She could be tough. You didn’t want her to think of you as “sentimental” or your writing as “saccharine”.

Though she was a partner in a publishing firm, and often rightly described as one of London’s best book editors, she never made much money. She lived in a flat rented from a cousin, the Economist journalist Barbara Smith, at the top of Smith’s house in Primrose Hill, and drove a small car. We paid mean advances for her books, and the approach of dependent old age loomed without the benefit of children or a big bank balance. But Somewhere Towards the End won a prize and became a bestseller. Diana could scarcely believe it: a book about being old was going to make it easier for her to be old. She had discovered a retirement home that was “astonishingly acceptable”, and with her new income she could afford to move in. As she wrote to me, it was “Bye-bye geriatric ward!!!” And it was.

I went to see her on Wednesday at a hospice in Belsize Park. Her final room – there she lay, aged 101, head back on the pillow and mouth open in a frozen yawn. Her silver hair had thinned but her skin was as clear as ever. We drew chairs to the bedside and talked, as people surrounding the apparently unconscious tend to do, hoping that she could hear even if she couldn’t speak. The talk was about her. Her nephew Phil remembered that she’d got frustrated with the lack of attention during a recent hospital visit and, unusually for her, pulled rank. “I write for the Guardian, you know,” she had said.

She breathed on. I took her hand briefly, and then Pru Rowlandson from Granta took it for the rest of her life. Diana made three or four sounds in her throat, and her eyes opened a little. Her breathing paused. Pru said her hand was cold. Dead or alive? It was hard to be sure, for a few minutes, and then it was certain. Phil closed her eyes.

Diana always remembered that her mother’s last words, having been asked about a visit to a nursery garden in Norfolk, were: “It was absolutely divine.” She hoped she would end her days with something similar in her mind’s eye. And it seemed that she had. It was the most serene transition: a small bird would have made more fuss.

• Ian Jack is a Guardian columnist