Hodgkin was born in Banbury, Oxfordshire, on 5 February 1914. He was the oldest of three sons of Quakers George Hodgkin and Mary Wilson Hodgkin. His father was the son of Thomas Hodgkin and had read for the Natural Science Tripos at Cambridge where he had befriended electrophysiologist Keith Lucas. Because of poor eyesight he was unable to study medicine and eventually ended up working for a bank in Banbury. As members of the Society of Friends, George and Mary opposed the Military Service Act of 1916 and had to endure a great deal of abuse from their local community, including an attempt to throw George in one of the town canals. In 1916 George Hodgkin travelled to Armenia as part of an investigation of distress. Moved by the misery and suffering of Armenian refugees he attempted to go back there in 1918 on a route through the Persian Gulf (as the northern route was closed because of the October Revolution in Russia). He died of dysentery in Baghdad on 24 June 1918, just a few weeks after his youngest son, Keith, had been born.