When Levy’s father was released in 1968, he was banned from working, and the family – Levy has an elder half-brother from her mother’s first marriage, as well as a younger brother and sister – had little option but to emigrate. Her father found work lecturing at Middlesex University, among other places. Money was tight. Her parents’ marriage ended in 1974. What Levy found in her writing was a way of giving her story a shimmering, attractive surface, while allowing her preoccupations with literary theory, myth and psychoanalysis to occupy its murkier depths. The novel can be taken as “a kind of holiday novel gone wrong”, she said – and it has been slipped into many a suitcase as a beach or poolside read. “I’m happy if the surface is read,” she told me. “Because everything else is there to be found. And I’m working hard for my readers to find it. But I don’t look down on readers who don’t. I think, ‘Something will come through.’” The “something” might include the Freudian desire and death-wish that suffuses the novel; its peculiar linked imagery of sugar mice and rats; above all the immense treacherous undertow of history – of the Holocaust, of 20th-century suffering and wars – that Levy sketches into the story with almost imperceptible strokes. To speak our life as we feel it is a freedom we mostly choose not to take, but it seemed to me that the words she wanted to say were lively inside her, mysterious to herself as much as anyone else. He was probably the wrong reader for her story, but I thought on balance that she might be the right reader for mine. Hot Milk frequently pans from the personal to the political. The waters of Almería’s beaches are infested with jellyfish, portentous refugees from a damaged ecosystem; Sophie ruminates on the conditions endured by local agricultural workers and the developing-world origins of various consumer goods; the privations of austerity economics are everywhere apparent. Indeed, the book’s preoccupation with kinship feels acutely relevant. In years to come, the profound societal impact of an ageing population will prompt more of us to reflect, like Sophie, on how a ‘wife can be a mother to her husband and a son can be a husband or a mother to his mother and a daughter can be a sister or a mother to her mother who can be a father and a mother to her daughter’. The plays and the novels Levy wrote in her 20s and 30s are collage-like, gravelly, spiky, and dense, marinated in the eastern European avant-garde influences she absorbed at college. She had a talent for epigrammatic, slightly surreal sentences. “I once heard a man howl just like a wolf except he was standing in a phone box in Streatham,” says a character in her first novel. But the work had not yet acquired the razored-away, spare quality that has given the later work such airiness, such ripple and flow, nor was there the emotional force with which readers identify so strongly.

But Swimming Home was rejected by every major publisher it was sent to. Levy, in all her certainty that it was good, was devastated. The years following the financial crisis of 2008 were inhospitable to a midlist novelist who hadn’t been in print for a while. The publishing industry was in trouble; the powerful new wave of feminism of the 2010s was a whisper rather than a roar; and the kind of spare, experimental books by women that would come to define recent literary trends, such as Cusk’s auto-fictional Outline trilogy, or Annie Ernaux’s intimate unfurling of memory, or Elena Ferrante’s revelatory novels on female friendship, had yet to appear in Britain. At the time, she said, “your book was either going to sell or it wasn’t going to sell, and when they said it was ‘too literary’, they meant it wasn’t going to sell”. Levy’s last novel, Swimming Home, was shortlisted for the Man Booker prize in 2012, having initially failed to find a publisher at all. Rejected for being “too literary” for the marketplace, apparently, it was taken up by And Other Stories, a subscription-based, not-for-profit publishing house. Since Hot Milk is being published by Penguin Random House, it seems fair to guess that the accolade of a Booker shortlisting has removed the presumed literary stain from this novel, which shares themes and obsessions with its predecessor. There is a sun-bleached, Mediterranean setting; explorations of troubled familial bonds, of the nature of sexuality, an examination of exile – and repeated motifs of incantatory language. “My love for my mother is like an axe,” Sofia says, more than once. “It cuts very deep.” This isn’t a long novel, but it is dense in the way a poem is dense, rich with meaning poured into its simple language Deborah Levy is a writer whose novels Swimming Home and Hot Milk were both shortlisted for the Booker Prize. Last year she published the final instalment of her ‘living autobiography’ trilogy of memoirs, and her earlier work includes plays for the RSC as well as short story collections and poetry. And so the book evolves into an experiment with truth and identity. This isn’t a long novel, but it is dense in the way a poem is dense, rich with meaning poured into its simple language. There seem to be no other patients at the Gómez clinic, its outer walls built from marble so that it resembles “a spectral, solitary breast”. Sofia becomes obsessed with a German seamstress, Ingrid Bauer, “whose body is long and hard like an autobahn”, and who stitches her a shirt with the word “beloved” sewn into its fabric – unless, of course, she has embroidered another word entirely. When Sofia is stung by jellyfish, a young man called Juan tends to her injury; she takes him as her lover, too. After a while she abandons her mother and Ingrid to visit her estranged father with his new young wife and baby in Athens, a broken city, even more damaged than Spain by economic collapse; her father, a wealthy man, confines her to a storeroom with no window and a camp bed that collapses as soon as she lies down on it.Levy (left) in 2012 with fellow Man Booker shortlisted authors Tan Twan Eng, Hilary Mantel, Will Self, Alison Moore and Jeet Thayil. Photograph: Luke MacGregor/Reuters The vase is a replica of an ancient Greek krater, a bogus reminder of Rose’s ex-husband, Sofia’s father, Christos Papastergiadis, who abandoned mother and daughter long ago. In the shards Sofia sees “the ruins that were once a whole civilisation”, an image of her mother’s shattered life. The broken vessel must be a sign, but of what? It is only one of many strange, lucid images that glitter through Levy’s novel, images that linger in the reader’s mind and won’t be chased away. It was not that easy to convey to him, a man much older than she was, that the world was her world, too. He had taken a risk when he invited her to join him at his table. After all, she came with a whole life and libido of her own. It had not occurred to him that she might not consider herself to be the minor character and him the major character. In this sense, she had unsettled a boundary, collapsed a social hierarchy, broken with the usual rituals. She could have stopped the story by describing the wonder of all she had seen in the deep calm sea before the storm. That would have been a happy ending, but she did not stop there. She was asking him (and herself) a question: do you think I was abandoned by that person on the boat?

August Blue will be published by Hamish Hamilton on 4 May, and is available at guardianbookshop.com Since 2011, and the publication of the Booker-shortlisted Swimming Home , Deborah Levy’s voice has boomed loud and clear across the dreary plains of literary Britain. Those who have seen her speak or read her work can testify that hers is a voice worth hearing – and has been, for years. A successful playwright in the early 1980s ( Pax , Heresies, The B File), Deborah Levy published her first novel Beautiful Mutants in 1989, the next step in a lifelong engagement with form, ideas, and most of all, language. ‘Her prose dazzles like sunlight on water,’ wrote one critic of Swimming Home – an appraisal that, applied to her entire body of work, stands up. Deborah was born in South Africa in 1959, the eldest child of anti-apartheid activists Norman and Philippa Levy. Her father was arrested when she was five and was imprisoned for four years. During this time, Deborah became an almost silent child, but was encouraged by a teacher to write down her thoughts, sparking her love of creative writing. After her father’s release, the family relocated to the UK and first lived above a menswear shop in London. As a teenager Deborah worked as a cinema usher, and a chance encounter with the film-maker Derek Jarman inspired her to change her plans to take a degree in literature, and instead she headed to Dartington College of Arts, where she studied writing for the stage and performance.Sofia, a young anthropologist, has spent much of her life trying to solve the mystery of her mother's unexplainable illness. She is frustrated with Rose and her constant complaints, but utterly relieved to be called to abandon her own disappointing fledgling adult life. She and her mother travel to the searing, arid coast of southern Spain to see a famous consultant - their very last chance - in the hope that he might cure her unpredictable limb paralysis. It was futile to try to fit an old life into a new life. The old fridge was too big for the new kitchen, the sofa too big for the lounge, the beds the wrong shape to fit the bedrooms. Most of my books were in boxes in the garage with the rest of the family house. More urgently, I no longer had a study at the most professionally busy time in my life. I wrote wherever I could and concentrated on making a home for my daughters. I could say that it was these years that were the most self-sacrificing, and not the years in our nuclear family unit. Yet, to be making this kind of home, a space for a mother and her daughters, was so hard and humbling, profound and interesting, that to my surprise I found I could work very well in the chaos of this time.