Cooper played Geoffrey Fisher, the stern father of the eponymous antihero Billy Liar, in both the original West End stage version (1960) and the later sitcom (1973–74). He also had a recurring role in Coronation Street as Willie Piggott, between 1964 and 1971. One of his other regular roles was as the caretaker Mr. Griffiths in the long-running children's TV series Grange Hill.