William Stewart Taor was born in Chesterfield, Derbyshire. The family moved to South London, where he attended Sutton Boys' Grammar School. He completed his undergraduate studies at Charing Cross Hospital Medical School and qualified as a doctor in 1962. He captained the medical school football team and played for United Hospitals. In 1962, he married classmate Pam Moss. He planned a career in radiology, but after joining Harrow Hospital as a resident surgeon under orthopedic surgeon Karl Nissen, he decided on orthopedics. Nissen named him his best house surgeon and Taor joined the orthopedic rotation at Charing Cross Hospital. In 1974 he became a consultant at Central Middlesex Hospital.