Hewett was born in Worthing, Sussex, to an army officer father and an Irish mother who was a descendant of Daniel O'Connell. He was educated at Beaumont College and at Wimbledon College, and at aged 7, made his acting debut in Dublin stage production of A Midsummer Night's Dream. At age 16, Hewett joined the Royal Air Force, leaving in 1940. Hewett then joined the Oxford Repertory Company and made his West End theatre debut in 1943.

Hewett made his film debut in the crime drama Pool of London (1951), and later appeared in roles on Robert Montgomery Presents and DuPont Show of the Month. He appeared as the grand theatre Director Roger DeBris in Mel Brooks's comedy film The Producers (1968). In 1976, Hewett played the generic bureaucrat Federov in the short-lived sitcom Ivan the Terrible. During the 1979-80 season, he played Captain Hook to Sandy Duncan's Peter Pan on Broadway. From 1983 to 1984, he portrayed Lawrence, Mr. Roarke's (Ricardo Montalbán) sidekick on the final season of the ABC series Fantasy Island.

He later appeared on Broadway in the musicals My Fair Lady, The Unsinkable Molly Brown, Music Is and Kean and in the plays Sleuth and The Affair, among others, and directed the 1960 Broadway revue From A to Z and the 1967 Off Broadway revival of the Rodgers and Hart musical By Jupiter. Hewett also directed several stage productions including The Marriage-Go-Round and Beyond the Fringe and Camelot.

The following year, Hewett landed his best known role as Lynn Aloysius Belvedere, an English butler who works for a middle class American family in the sitcom Mr. Belvedere. After the series ended its run in 1990, Hewett appeared in a guest spot on an episode of the NBC teen sitcom California Dreams in 1994. His last onscreen role was a cameo appearance on the Fox series Ned and Stacey in 1997.

Hewett died on 3 August 2001, at his Los Angeles home from complications of diabetes. He was 80 years old.