He was born Lewis Ernest Watts Mills in the East Suffolk town of Felixstowe on February 22, 1908 and began performing with amateur theater groups in his teens. At age 19, Mills moved to London and enrolled in Zelia Raye's Dancing School, appearing in the chorus of The Five O'Clock Revue before embarking on a tour of the Far East with a repertory company called The Quaints. In Singapore, he met Noël Coward, who later cast him in a London production of Charley's Aunt and the original productions of Cavalcade and Words and Music. In 1932, Mills made his film debut in The Midshipmaid; by the end of the decade, he was appearing in such films as Tudor Rose and Goodbye Mr. Chips.
Mills also appeared in West End productions of She Stoops to Conquer, A Midsummer Night's Dream, Of Mice and Men, and three plays written by his wife Mary Hayley Bell: Men in Shadow, Duet for Two Hands, and The Uninvited Guest. His Broadway credits include the 1961 production of Ross (for which he received a Tony Award nomination) and the 1987 revival of Pygmalion that starred Peter O'Toole.
He won an Academy Award for his performance in the 1970 film Ryan's Daughter. Mills appeared in more than 100 movies over the course of his seven-decade career, including The Colditz Story, In Which We Serve, Dunkirk, Scott of the Antarctic, and Tunes of Glory. Though he was left nearly blind after both of his retinas failed in 1992, he continued acting, appearing notably in Bright Young Things (2003) as "Man Taking Cocaine at Party."
Mills was named a Commander of the British Empire in 1960 and was knighted in 1976. He is survived by his wife, playwright Mary Hayley Bell; his son, Jonathan; and his daughters Juliet and Hayley, both of whom are well known actresses.