This Boy: a Memoir of Childhood, By Alan Johnson. Bantam, £16.99

At the funeral of Alan Johnson's mother, who died in 1964 when he was 13, his father did him two favours. He gave him a small present, a key-ring with a miniature football attached, and he bade him farewell, forever. Young Alan had the kind of father whom D H Lawrence might have thought too over-the-top for fiction. It is not from a researcher's file that the former home secretary draws his knowledge of domestic violence, but from witnessing his drunken dad punching his mother.

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This irresponsible womaniser gambled in a day what his poor wife earned as a skivvy in a week; there was one terrible Christmas when he left her in hospital for the company of another woman, leaving his children alone to burn the dinner. Yet This Boy is not a misery memoir or revengeful read. The way Johnson tells it, in straightforward, unsentimental prose, it is a lively account of a close-knit family of three.

His mother shines out as a saintly woman who struggled against a disastrous husband, chronic illness and extreme poverty in a Notting Hill slum. His sister Linda, three years older, was even more of a fighter. Having always looked after her brother while their mother was working or in hospital, she found herself at 16 about to lose him to a foster family. Plus their house was to be demolished.

In the damp, squalid building condemned 20 years before his birth, the family rented two rooms: "One for sleeping in and one for eating in." They shared the front door and toilet in the yard with five families. Declaring that she and Alan would otherwise stay put even if the place was pulled down about their ears, Linda persuaded a worried social worker to wangle them a council flat – together. And then she rejected the first one she was offered, a stinking dump.

Orphan Alan carried on at school, with Linda attending parents' days. As the book ends when he is 18 (and married) we don't know what happened to his remarkable sister. We know that he reached the Cabinet and has become one of our most likeable politicians – and the author of this engaging book.