WH Auden once said that writing about your life was “using up capital”, but this is what makes memoir such a generous form. And Deborah Levy is a most generous writer. What is wonderful about this short, sensual, embattled memoir is that it is not only about the painful landmarks in her life – the end of a marriage, the death of a mother – it is about what it is to be alive.

I can’t think of any writer aside from Virginia Woolf (or, perhaps, Helen Simpson) who writes better about the liminal, the domestic, the non-event, and what it is to be a woman. I always feel, reading Levy (this is her second memoir), that she is a writer with nothing much – and with everything – to say.

After her marriage breaks down – at a time when her career is ascending (she has been shortlisted for the Booker prize) – Levy and her two young daughters move into a north London block of flats which she describes, in its stricken deficiency, with panache. She makes of the flat a story, with its big skies and its sterile corridor (which, with playful perversity, she names the “corridor of love”). She describes the bees that are her unexpected flatmates, her prospering strawberry plants, and the exotic oranges with cardamom that she and her daughters eat for breakfast. She writes entertainingly about her attempt, encouraged by a friend, at “living with colour” – her yellow bedroom a garishly false move.

Levy’s style is shorn; emotional burdens are carried without surplus words. She describes renting the poet and playwright Adrian Mitchell’s shed from his widow, to write in, and it becomes, like the flat, a character: a shed of one’s own. The affectionate portrait of eightysomething Celia Mitchell herself is delightful. She wonders why Levy bothers to wear pearls to work in a dirty shed, and introduces her to friends as “She Who Lurks in the Garden”.

This is a little book about a big subject. It is about how to “find a new way of living”. Rage is brewing just beneath its surface. But it’s complicated, not least because Levy has a gift for homemaking. She writes about it as a process of “empathy” (she uses the word more than once), and reflects that it is “an act of immense generosity” in women to “be the architect of everyone else’s wellbeing”.

How, then, in middle age, does a woman who possibly never felt at home in her own home leave? How does she attain the same freedom as a man? How does a writer stay a mother? Levy notes the telltale way in which wives often get talked about by their husbands as “my wife” – and are not named.

I read this book with indecent speed and greed, but it deserves to be read at a pace closer to lived time. I particularly love Levy’s amused curiosity about strangers. I was entertained by the saga of the elderly neighbour who did not like her parking her electric bicycle in front of their flats. This apparently insignificant conflict was an insight into one woman unable to watch another living a fuller life (my judgment – Levy shows but does not judge).

I was stirred by the portrait of her mother, and the description of buying ice lollies from a Turkish newsagent’s during her mother’s last days in hospital, when these were all she could eat. One disastrous day the newsagent’s had only bubblegum flavour left. Levy was distraught – but the story of the predicament made her mother smile. Levy was too devastated to explain in the shop why, in midwinter, she was buying ice lollies every day – until after her mother’s death. And then the newsagents were “so upset it was their turn not to speak”. This made me cry, although I was not surprised by their reaction: Levy knows how to share her story.

• The Cost of Living by Deborah Levy is published by Hamish Hamilton (£12.99). To order a copy for £11.04 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99