Born in Derbyshire, Bates earned a scholarship to the Royal Academy of Dramatic Art in London, where he studied before leaving to join the Royal Air Force. In 1956, he debuted on stage in the West End, starring in Look Back in Anger, a role which made him a star. Four years later, he appeared in The Entertainer, his first film role. He soon starred in Whistle Down the Wind, and in the Bernard Malamud film The Fixer, which gave him an Academy Award nomination for Best Actor.
Bates starred in such international hit films as Georgy Girl, Far From the Madding Crowd, Zorba the Greek, An Unmarried Woman and Women in Love, but he consciously decided to concentrate on a few well-defined roles, rather than to take everything that came his way. On television, his parts ranged from classic roles such as The Mayor of Casterbridge (1978) to Guy Burgess in An Englishman Abroad (1983) to the storyteller in the 2000 version of the Arabian Nights.