Daughter of John Percival Postgate and Edith Allen, Margaret was educated at Roedean School and Girton College, Cambridge. While at Girton, through her reading of H. G. Wells, George Bernard Shaw and others, she came to question the Anglicanism of her upbringing and to embrace atheism, socialism and feminism. On successfully completing her course (Cambridge did not allow women to graduate formally until 1947), Margaret became a classics teacher at St. Paul's Girls' School.
During World War I, her brother Raymond sought exemption from military service as a socialist conscientious objector, but was denied recognition and jailed for refusing military orders. Margaret's support for her brother led her to a belief in pacifism. During her subsequent campaign against conscription, she met G. D. H. Cole, whom she married in 1918.
The couple worked together for the Fabian Society before moving to Oxford in 1924 where they both taught and wrote. In the early 1930s, Margaret abandoned her pacifism in reaction to the suppression of socialist movements by the National Socialist governments in Germany and Austria and to the events of the Spanish Civil War.
In 1941, she was co-opted to the Education Committee of the London County Council, on the nomination of Herbert Morrison, and became a champion of comprehensive education. She was a member of the Inner London Education Authority from its creation in 1965 until her retirement from public life in 1967.
She wrote several books including a biography of her husband. Margaret's brother Raymond was a mystery novelist and the couple jointly authored many mystery novels. A list of these can be found under G. D. H. Cole's entry.