Heinemann was educated at Roedean School and at King Alfred School in London, and read English at Newnham College, Cambridge from 1931, later graduating from Cambridge University with a Bachelor with first class honours.
She was the lover of John Cornford, while a student at the University of Cambridge. The historian Eric Hobsbawm, who was also there at the time, wrote "she probably had more influence on me than any other person I have known."
She joined the CPGB in 1934, because of its active opposition to the British Union of Fascists. After Cambridge she taught 14-year-old girls at Cadbury"s Continuation School in Bournville, now Bournville College, on day release from the chocolate factory.
In the CPGB she worked in the Labour Research Department from 1937.
She stood as the communist candidate for Vauxhall Constituency in the 1950 General Election. In 1959 she resumed teaching at Camden School for Girls and then Goldsmith"s College from 1965-1977.
In 1976 she was made a Fellow of New Hall, Cambridge. She was still teaching at New Hall up to 1989 and stayed with the CPGB until it was dissolved in 1991.