He was born in Cambridge, and named after Rupert Brooke, who was a friend of his parents, but preferred to use his second name. He was educated at Stowe School and Trinity College, Cambridge. As an undergraduate, reading history, he joined the Communist Party of Great Britain. He was two or three years younger than the group of Trinity College communists including Guy Burgess, Donald Maclean, Kim Philby and James Klugmann.
Another Cambridge student, who would play a major part in his life, was Margot Heinemann. They were lovers, and he addressed both poems and letters to her. He also had a relationship with a Welsh woman, Rachel (Ray) Peters, with whom he had a child: James Cornford, who was subsequently adopted and brought up by his grandparents, Francis and Frances Cornford. A photograph of Peters and Cornford can be found at the National Portrait Gallery, London.
From 1933 he was directly involved in Communist Party work, in London, and became associated with Harry Pollitt. At the start of the Spanish Civil War he travelled to Barcelona, and volunteered and briefly served with the POUM militia, before returning to England, where he recruited a number of volunteers. With this group he travelled to Paris and then on to Albacete, where they joined the International Brigades. He served with a machine-gun unit of the Commune de Paris Battalion, and fought in the defence of Madrid through November and December 1936. Having transferred to the recently formed British Battalion, he was killed in uncertain circumstances at Lopera, near Córdoba. A memorial volume to Cornford was published in 1938. As Stephen Spender observed in his review of the book, "Cornford's life speaks for itself in a way that burns the imagination ... The fact that Cornford lived and that others like him still live, is an important lesson to the leaders of democracies. It shows that people will live and die and fight for democracy if it gives them the justice and freedom which are worth fighting for." 
Cornford's poem Full Moon At Tierz (1937) is a literary expression of the anti-fascist cause.
His brother Christopher Cornford continued to be active in politics until well into the 1980s.
In poetic terms, he was no modernist; as George Orwell pointed out in 1940, he represented continuity with the older, imperial tradition.