Cooke was educated at Wyggeston Grammar School and Christ Church, Oxford He became a Research Lecturer at Christ Church in 1939. During World War Two he conducted Radar research for the Admiralty. He was a Fellow of New College, Oxford, from 1946 to 1976; University Lecturer in Physics from 1944 to 1971; Reader in Physics from 1971 to 1976; and Warden of New College from 1976 to 1985.