He was born Richard Carey Winter, the third of four sons, at Meopham, Kent, and made his film debut in Franco Zeffirelli's 1968 production of Romeo and Juliet in the role of Gregory. Subsequent films included If...., Nicholas and Alexandra and the first film by Derek Jarman, Sebastiane.
On television, he was best known for his roles in the sitcom Please Sir!, as one of the main character's teaching colleagues, and in the London Weekend Television comedy A Fine Romance, as the brother-in-law of Judi Dench's character. He also played Uncas in the television series The Last of the Mohicans (1971). His last role before his AIDS-related death was as John (the servant) in Zeffirelli's 1996 adaptation of Jane Eyre.
He died in 1997 aged 52. In an obituary, The Daily Telegraph quoted If... director Lindsay Anderson: "I never met a young actor like Richard! Without a touch of vanity, completely natural yet always concentrated, he illumines every frame of the film in which he appears."
- Romeo and Juliet (1968) - Gregory
- If.... (1968) - Wallace: Crusaders
- The Bed Sitting Room (1969) - Allan
- First Love (German title: Erste Liebe) (1970) - Lt. Belovzorov
- The Breaking of Bumbo (1970) - Bumbo
- Nicholas and Alexandra (1971) - Grand Duke Dmitry
- Alice's Adventures in Wonderland (1972) - 7 of Spades
- Confessions of a Pop Performer (1975) - Petal (Kipper)
- Sebastiane (1976) - Justin
- International Velvet (1978) - Tim
- Mannen i skuggan (1978) - Tornilla
- The Tempest (1979) - Antonio, his brother
- My Favorite Year (1982) - Technical Director
- Johnny Dangerously (1984) - Prisoner
- White Hunter Black Heart (1990) - Basil Fields, British Partner
- Hamlet (1990) - Bernardo
- The Lost Language of Cranes (1992) - Frank
- Jane Eyre (1996) - John (Last appearance)
- "Richard Warwick". BFI.
- "Richard Warwick: actor admired by Noel Coward, Lindsay Anderson and Zeffirelli". The Daily Telegraph. London. 19 December 1997.