In his essay “Why I Write”, George Orwell looked back to the childhood springs of his writing: “I knew that I had a facility with words and a power of facing unpleasant facts.” I have thought of that line a few times reading Jenny Diski. For 30 years she has been one of the most individual, wildly various writers in English literature, a prolific author of novels, short stories, reviews, essays, travelogues, memoirs – though part of the individuality is that she makes those distinctions between genres or forms seem flimsy and artificial: “It’s all writing.”

Over the last year and a quarter, Jenny (we’re friends, I think: don’t imagine this is an objective appraisal) has been writing a series of monthly articles in the London Review of Books that have won her a new set of readers, and a new level of admiration from her fans. The pieces were occasioned by two deaths. The first was Doris Lessing’s, two years ago, at the age of 94. In 1963, Jennifer Simmonds was a difficult, scared 15-year-old: the boarding school to which she had been sent by the local council had expelled her, she had run away from her parents (who had abused her in ways that seem both absent-minded and creative), she had been raped by an American stranger in London, she had tried to kill herself with an overdose of Nembutal, and was now confined to a psychiatric unit in Hove. A former schoolfellow, Peter Lessing, told his mother about this scandalous girl, and Doris, already famous as the author of The Grass Is Singing and The Golden Notebook, wrote to her, offering a home – an act of enormous generosity, but with tightly prescribed limits: home never came with guarantees of security, or love. Still, their relationship – not quite parental, not quite friendly – lasted 50 years; and though Lessing put fictionalised Jennys into several of her novels, Jenny did not feel able to write about Lessing while she was alive.

The second death is Jenny’s own. In July 2014 she was diagnosed with lung cancer and given two or three years to live. Her characteristic response was to crack a Breaking Bad joke, then settle down to figure out how she could write about it. What she has been producing is in some ways the conventional cancer diary, moving from diagnosis and rejection of the cliches of cancer writing, the “battle” and “bravery”, to treatment (for Jenny, “poison infusions” and “death rays”) and descriptions of tiredness, pain, side effects, encroaching sadness. But she has turned this into something funnier, livelier and more complicated, the pain woven together with memories of Doris, her childhood, the freedoms and demands of the 60s, of the writing life. Ideas and images flit over the page with unabated rapidity – Joyce, Nabokov, Don Giovanni, Bruce Forsyth, Stephen King. Sometimes the rhythm of the story becomes more urgent; you itch to know what happens next. And throughout, Diski refuses to soften her own edges, to make herself seem kinder or less narcissistic: she won’t turn away from unpleasant facts, particularly about herself. The consequence of this hardboiled attitude is that when she does grieve – foreseeing the loneliness of her husband, the poet and academic Ian Patterson, her two small grandchildren growing up with no memory of her – the effect can be almost overwhelming.

Doris Lessing, left, and Jenny Diski in 1963

Since the diagnosis, things have not gone well: the death rays left her with radiation burns and exacerbated the pulmonary fibrosis she already had; now it seems that this, rather than the cancer, is most likely to see her off. Other side effects have included a tendency to fall over, weight gain with hamster face (“They put me on steroids which made me look like a mongoose, and fatter and fatter as the minutes go by” – before all this she was vain of her slender prettiness) and, for a couple of weeks early this summer, going doolally enough to raise suspicions of a brain tumour; naturally, she has had periods of depression. But though she was slowed down by the chemo, and by a broken wrist from one of her falls, and has to work in bed because the effort of getting up and dressed exhausts her for the day, she swigs from a bottle of morphine and keeps writing. She says writing comes easily to her, or at least sentences do (finding the right structure is the part that worries her); but this was not always so, and it’s a surprise to find that someone who has published so much – 18 books, countless articles – started her writing career late.

She can remember wanting to be a writer when she was a child, “because I was a reader, and I was very solitary”: she asked for a typewriter one Christmas, with some idea of becoming a reporter, and was furious at being presented with a toy with keys that stuck (this was when her parents still had money, her father having done well on the black market in the war). Then in her teens, living with Lessing, she found herself in the company of writers: Alan Sillitoe, Ruth Fainlight, Naomi Mitchison, Ted Hughes, Arnold Wesker, Christopher Logue. Henry Williamson, of Tarka the Otter fame, told her: “You are a swallow among the starlings, my dear.” Robert Graves came to dinner and she couldn’t speak; afterwards he asked “who that attractive young Russian girl was, and what a pity it was that she spoke no English”. But for a long time, everything she wrote ended up in the bin (“The sound of the voice in my ear as I typed, repeating ‘this is crap, this is crap’”), and a lot of other things happened: she dropped out of school, spent more time in a psychiatric ward, took drugs in a flat in Covent Garden, helped set up a free school in Camden, trained as a teacher and taught at a comprehensive in Hackney. She married, briefly, Roger Marks and came out of it with a flat, a daughter and the shared surname they had concocted. Pregnancy gave her an excuse to leave teaching; she started an anthropology course at University College London, but after two years had “what I suppose must be called a breakdown” and dropped out: “And everybody said, ‘Ooh look at Jenny, she always leaves things, she never finishes anything’ – which is what all the grown-ups who knew me knew about me.”

But in her late 30s she finished a novel, Nothing Natural (1986), about a woman who becomes involved in a sadomasochistic relationship. I’ve read on the web that as a result of the novel Jenny was banned from writing for Spare Rib; she says that’s not true, though she was barred from a feminist bookshop in Islington. In some ways it is her most conventional book – chronologically straightforward, set in a naturalistically described contemporary London, with an air of thrillerish suspense (it is possible that the male half of the central relationship is a rapist). In a way, Nothing Natural is just as much an erotic wish-fulfilment fantasy as any Barbara Cartland novel; but even after 50 Shades of Grey made S&M acceptable, Nothing Natural is disturbing: there is no sense that the heroine can pierce the carapace of male cruelty to find the wounded creature within, or that she’d want to if she could. What she wishes for is pain and degradation.

Though that book is not typical, you can see some of Diski’s distinguishing marks: a lovely sentence-by-sentence clarity, and an absence of embarrassment – something particularly noticeable in her memoirs. Perhaps she is unembarrassed because she lacks those crippling English class sensitivities – her parents were the children of East End Jews who’d emigrated from Russia and Poland, the first generation born in England, and she says “I never knew where I was exactly. I knew where everyone else was exactly, but I was sort of Jewish and English.” But she, says, too, “I’ve never had a sense that privacy has anything to do with people knowing things about you.

‘People write to me sometimes, and they say that they know me. And of course I know they don’t know me … There is a need for readers to have a sort of personal relationship with writers, which is why you get so much shit” – she spits the word out – “about whether a book is good. Are the characters believable? Or is the plot good? The mediocrity of fiction is really to do with feeling cosy, and that you’ve got a nice friend sitting in your lap telling you a nice story. I’ve never been a nice friend sitting in anyone’s lap. I just wanted to write stuff down in shapes, really.”

I never knew where I was exactly. I knew where everyone else was exactly, but I was sort of Jewish and English

After Nothing Natural the novels came fast, and stranger. When Lessing came to the UK from Africa she told an interviewer that the British novel was “small, well shaped and with too much left out”. Diski’s writing has never left much out, and is rarely small. Nony, who narrates Like Mother (1989), is an anencephalous baby, born without a brain, who tells her mother’s story in conversation with an interlocutor who is explicitly non-existent (when I asked Jenny what novel of hers I should start with, she said she thought Like Mother “works”). In Happily Ever After (1991), 68-year-old Daphne drugs the much younger Liam and straps him to a bed so that she can seduce or rape him, with the result that, just as she had expected, he falls deeply in love with her. Much of Monkey’s Uncle (1994) takes place in an imaginary landscape where Charlotte, middle-aged and mad, converses with Freud, Marx, Darwin and a talking orang-utan. It is hard to pin down precisely what happens in The Dream Mistress (1996), even how many protagonists there are; Eileen Battersby in the Irish Times called it “disturbingly erotic”, though an inference from Jenny’s fiction is that this is a tautology: if it isn’t disturbing, it isn’t erotic). In Only Human (2000), God gets involved in a love triangle with Abraham and Sarah – Jenny seems ambivalent about how much her Jewishness matters, and doesn’t believe in God, but the God she’s not believing in is always Old Testament: even in fiction, she doesn’t go along with the idea that He is love.

Meanwhile, she started writing for the London Review of Books (only because the then-editor, Karl Miller, was flirting with her publisher at a party, she says), and became one of its stars. Those weeks when the paper felt oppressively dry or cliquish, you would turn with relief to Diski, knowing you would get wit and scepticism couched in lucid, frank prose: an assault on the risible, nannying eroticism of Madonna’s would-be porn book Sex, a dazzling argument about the genius and narrowness of Dennis Potter, or a skewering of Anaïs Nin. She became a totem, what EB White was to the New Yorker or Auberon Waugh to Private Eye. (The first few years of her writing for the LRB are collected in Don’t, 1998.)

Jenny Diski at her home with her husband, Ian Patterson. Photograph: Gary Calton

Although she doesn’t distinguish between different kinds of writing, the turn to non-fiction with Skating to Antarctica (1997) marked a change, if only because it was possible to see how much truth lay behind what had been presented as fiction. More than once in memoirs she’s recalled the day bailiffs came to the flat she lived in off Tottenham Court Road, after her father had left and the money was gone: though they weren’t evicted, her mother took her by the hand and dragged her through the streets, shouting that they were destitute and would have to live under the arches at Charing Cross. The story also happens in Like Mother. A theme of Skating to Antarctica – at one level, a humorous travelogue about a cruise to the Antarctic – is Diski’s desire for whiteness, blankness, oblivion: she had given that need to characters in her short story collection The Vanishing Princess (1995), and to Nony’s mother in Like Mother – at the end of the book, she is content to be diagnosed with terminal cancer. I mention the painful irony to Diski, who says: “I was always good at prophecy.”

Stranger on a Train (2002) is another travelogue-cum-memoir, about two train journeys, “daydreaming and smoking around America”. What I Don’t Know about Animals (2010) is a joky-profound consideration of our place in nature, what other species can mean to us – again, mixed with autobiography, memories of beloved cats and neglected goldfish: “I start with me, and often enough end with me,” she wrote last year. “What else am I going to write about but how I know and don’t know the world?” In this respect, her teacher is Montaigne – who provided the epigraph for her 2006 book of essays, On Trying to Keep Still, and is at the centre of her novel Apology for the Woman Writing (2010) That book tells the story of Marie de Gornay, a real person, an obsessive woman who became the great writer’s sort-of daughter: you might take that as more autobiography; I couldn’t possibly comment.

That was her last novel. There is one more book to follow – the cancer diary, which she will edit when enough of it is written: 70 or 80,000 words so far. It promises to be the best thing she has produced, but it will mark an end. And for that reason, I can’t think of a book I’ve looked forward to less.