The son of a general practitioner, William Woodward was educated at the Sydney Church of England Grammar School from 1933-38, where he was a keen all-round sportsman, competing at rugby, shooting, rowing and boxing. Woodward then went to Sydney University in 1939, to study medicine. However, in 1942, Woodward and a friend went to a services recruiting office and were enlisted into the second Australian Imperial Force, and later, into the Australian Field Ambulance. Invalided out in 1944, he got back to full fitness after joining the Sydney Rowing Club. He also returned to his studies at Rhodes College, before moving to England, and going to Brasenose College, Oxford. During his time at Oxford, he won a Blue in the 1948 Boat Race, and was in the Oxford coxed fours at the London Olympics later that year. Woodward returned to Australia to complete his studies and became a surgeon. He pioneered chest surgery in Tasmania, and carried out the first open heart operation in the island. He returned to England, after some personal problems in 1966, and it became his new home.