Born in Torquay, he was educated at the University of Cambridge. There he became involved with the Footlights Club, of which he later became president. After graduating he created the comedy stage revue "Beyond the Fringe", beginning a long-running partnership with Dudley Moore. In 1961, Cook opened the comedy club The Establishment in Soho, Central London. In 1965, Cook and Moore began a television career, beginning with "Not Only... But Also". Following the success of the show, the duo appeared together in films "The Wrong Box" (1966) and "Bedazzled" (1967). Cook and Moore returned to television projects continuing to the late 1970s, including co-presenting "Saturday Night Live" in the United States. From 1978 until his death in 1995, Cook no longer collaborated with Moore but continued to be a regular performer in British television and film.