Baker was born in Scotland Road, Liverpool, England. His mother, Mary Jane (née Fleming), was a cleaner, and his father, John Stewart Baker, was a Jewish/English sailor who was rarely at home. His parents were working class Liverpudlians. Baker left school at 15 to become a Roman Catholic monk, and remained in this lifestyle for six years, but left after losing his faith. He did his national service in the Royal Army Medical Corps, serving from 1955 until 1957. At the same time, he took up acting, first as a hobby but he turned professional towards the end of the 1960s.
- He played Rasputin in Nicholas and Alexandria (1971)
- He was perhaps best known for playing the Fourth Doctor on Doctor Who.