A fencer with the Salle Paul, Harry Cooke won the club foil championship in 1935-36 and 1938, before winning the British foil title in 1939. He finished joint third in his first defence of the title in 1947, before regaining it in 1951, when he won all five contests in the final pool. He won the British Foil Team Championship with the Salle Paul on many occasions. The Salle Paul was founded in 1932, and named after its founder, Léon Paul, and Harry Cooke was their first pupil. Cooke won a foil bronze medal for Great Britain at the 1955 World Championships in Roma, and at Cardiff in 1958, when he was 51 years of age, he won the gold medal for England in the team foil event with the brothers Raymond and René Paul.