Hewett was born in Worthing, Sussex, to an army officer father and an Irish mother who was a descendant of Daniel O'Connell. He was educated at Beaumont College and at Wimbledon College, and at aged 7, made his acting debut in Dublin stage production of A Midsummer Night's Dream. At age 16, Hewett joined the Royal Air Force, leaving in 1940. Hewett then joined the Oxford Repertory Company and made his West End theatre debut in 1943.