He originally trained to be an accountant in New Zealand, but decided to change his career path in 1950 when he made his stage debut as Sebastian in Twelfth Night. He moved to London in 1950 and studied acting there at the Old Vic Theatre. He appeared in The Shakespeare Memorial Theatre Company’s celebrated 1956–1958 season of productions in Stratford, which included Hamlet, Love’s Labour’s Lost, The Merchant of Venice, Julius Caesar and The Tempest. He went on to have such varied stage roles as Bob (narrator) in Irma la Douce, Ratty in Toad of Toad Hall and Jean-Paul Marat in Marat/Sade.

He made his Broadway debut in 1952, playing Sam Weller in The Pickwick Papers, and subsequently appeared in Irma La Douce, The Incomparable Max and Oliver!, for which his Fagin was nominated for a Tony Award. He is also known for his roles in the operettas of Gilbert and Sullivan, on both stage and television. He starred in the first national tour of the musical Drood, replacing George Rose, who was murdered during the run.

In the 1978 television miniseries Centennial, he played the Scottish accountant Finlay Perkin. He played both Ko-Ko (the starring role) in The Mikado, and the title character, John Wellington Wells, in The Sorcerer for the Brent Walker television series of Gilbert and Sullivan productions, shown by the BBC in 1983.

Revill is known for his proficiency with accents. He is also known for his voice work in feature-length films and animated series, which includes Alfred Pennyworth in the first three episodes of Batman: The Animated Series, the voice of Chico in the seven episodes of Chico the Rainmaker (The Boy with the Two Heads) (1974), the voice of Emperor Palpatine/Darth Sidious in the original 1980 version of The Empire Strikes Back (he was later replaced by Ian McDiarmid in the 2004 DVD version though Revill is still credited) numerous cartoons such as The Transformers, Batman: The Animated Series and DuckTales and more video games, including Marvel: Ultimate Alliance and Conquest: Frontier Wars.