Trained at the Royal Academy of Dramatic Art, Mills began his career onstage, landing a big break in 1929 when he portrayed the title character in Hamlet at London's Old Vic Theatre to great acclaim. He subsequently starred in the U.K. in many other Shakespearean pieces, Of Mice and Men, three plays written by his wife, Mary Hayley Bell Men in Shadow, Duet for Two Hands and The Uninvited Guest, and much more. He made his Broadway debut in Ross, earning a 1962 Tony nomination for Best Actor in a Play. He also starred in Pygmalion on the Great White Way in 1987.
Mills also made his mark on the big screen. He won a 1971 Academy Award for his supporting performance as a mute in Ryan's Daughter. His other film credits include Those Were the Days, The Ghost Camera, The River Wolves, A Political Party, Blind Justice, Doctor's Orders, Charing Cross Road, Tudor Rose, Goodbye, Mr. Chips, Dangerous Comment, The Black Sheep of Whitewall, The young Mr. Pitt, Great Expectations, The Long Memory, Hobson's Choice, The End of the Affair, Above Us the Waves, War and Peace, Around the World in Eighty Days, Swiss Family Robinson, The Chalk Garden, The Family Way, Oh! What a Lovely War, Dulcima, Trial by Combat, The Big Sleep, Gandhi, Sahara, Who's That Girl, The Big Freese, Hamlet and Bright Young Things. Mills was made a Companion of the Order of the British Empire in 1960 and knighted in 1976.