Keuneman was educated at the Royal College, Colombo where he was the head of the junior cadet platoon, prefect, captain of the debating team and president of the literary association. He won college colours at rugger and won the Dornhorst Memorial Prize and the Shakespeare prize. He went on to Pembroke College, Cambridge in 1935 where he became a communist, President of the Cambridge Union and editor of the student magazine "Granta". He gained a BA Tripos in History, Sociology and English Literature and joined the Gray's Inn to study law leaving without taking his bar examinations. Later he gained a MA from Cambridge.