Kerr was born in Berlin but left Germany with her parents and her brother, Michael Kerr, in 1933, soon after the Nazis first came to power. They were forced to leave as her father, noted drama critic, journalist and screenwriter Alfred Kerr, had openly criticised the Nazis. His books were burned by the Nazis shortly after the family fled Germany. They travelled first to Switzerland and then on into France, before finally settling in the UK, where she has lived ever since. She subsequently became a naturalised British citizen.

During the Second World War, Kerr worked for the Red Cross, before becoming an artist. She was later prompted by her future husband ... scriptwriter Nigel Kneale ... to apply for a job as a BBC television scriptwriter. She got the job and she and Kneale were married in 1954; they remained married until Kneale's death in 2006. They had two children: their son Matthew Kneale is a distinguished writer himself, winning the Book of the Year prize at the prestigious Whitbread Book Awards in 2000 for the novel English Passengers. Their daughter, Tacy Kneale, works in the special effects industry, and has worked on the popular Harry Potter films. Tacy plans to begin writing children's books also.

Kerr is best known for her children's books. Although she dreamed of being a famous writer as a child, she only started writing and drawing books when her own children were learning to read. She has written self-illustrated picture titles such as the 17-strong Mog series and the highly successful The Tiger Who Came To Tea. She has written novels for children such as the autobiographical When Hitler Stole Pink Rabbit and "The Other Way Round", which semi-autobiographically tell the story of the rise of the Nazis in 1930s Germany from a child's perspective. Again it was her children that occasioned this writing: when her son was eight he saw The Sound of Music and remarked "now we know what it was like when Mummy was a little girl". Kerr wanted him to know what it was really like and so wrote When Hitler Stole Pink Rabbit.

Kerr lives in Barnes, London, the same house she has lived in since 1962. She says that since the death of her husband writing has become more important than ever and she continues to write and illustrate new children's books with Twinkles, Arthur and Puss published in 2008 and One Night in the Zoo in 2009.

She won the Deutscher Jugendliteraturpreis in 1974 for her young adult novel When Hitler Stole Pink Rabbit.