Born in West Derby, England, made his acting debut in 1911 in regional vaudeville before moving to London to appear at the "Vaudeville Theatre" in 1914. He served in the British Army during World War I where he received injuries that left his face partially scarred and paralysed. In his acting career he would use this injury to good effect, by showing the unblemished side of his face when playing comedy or romance, and the scarred, paralysed side of his face when playing drama or tragedy. After the war, Banks joined the Birmingham Repertory Theatre. He returned to London in 1921 and established himself as a leading dramatic actor known for his powerful yet restrained performances.

His first important film role was in The Most Dangerous Game (1932) as a diabolical "human hunter" with Joel McCrea and Fay Wray and for the rest of his career he divided his time between Britain and the United States, and between film and theatre. His other film roles include Alfred Hitchcock's The Man Who Knew Too Much (1934), Fire Over England (1937), Jamaica Inn (1939), The Arsenal Stadium Mystery (1939), Went the Day Well? (1942) and Laurence Olivier's Henry V (1946).

His theatre roles included Eliza Comes to Stay (his American debut in 1914), Captain Hook in Peter Pan (1924), Petruchio in The Taming of the Shrew (1937), and the schoolmaster in Goodbye, Mr Chips (1938).