Annis played the Widow of the Web in the 1983 science fantasy film "Krull", and starred as Lady Jessica in the 1984 David Lynch science fiction film "Dune". She appeared as Tuppence with James Warwick as Tommy in "The Secret Adversary" (1983) and the subsequent series, "Agatha Christie's Partners in Crime" (1983–84). Annis played Jacqueline Kennedy in "Onassis: The Richest Man in the World" in 1988. She portrayed Mrs. Wellington in the second film and directorial debut by Prince, "Under The Cherry Moon" (1986).