After the war, Morris signed a three-year contract as a camera operator with Independent Producers based at Pinewood Studios. Among the films he worked on during this tenure include Sidney Gilliat's "Green for Danger" (1946) and two David Lean features, "David Copperfield" (1948) and "The Passionate Friends/One Woman's Story" (1949). Morris was promoted to director of photography with Ronald Neame's "Golden Salamander" (1949). In 1952, he began a collaboration with director John Huston that lasted over twenty years and included such distinguished efforts as "Moulin Rouge" (1952), "Beat the Devil" (1953) "Moby Dick" (1956), uncredited work on "Reflections in a Golden Eye" (1967) and "The Man Who Would Be King" (1975).
Once Morris' reputation was established in the early 50s, he went on to work with some of the world's best directors on such films as Carol Reed's "The Key" (1958) and "Our Man in Havana" (1960), Tony Richardson's "Look Back in Anger" (1959) and "The Entertainer" (1960), J. Lee Thompson's "The Guns of Navarone" (1961), Stanley Kubrick's "Lolita" (1962), Franco Zeffirelli's "The Taming of the Shrew" (1967), and Joseph L. Mankiewicz's claustrophobic "Sleuth" (1972). In the mid-60s, he won three consecutive British Academy Awards for his evocative black-and-white work on Jack Clayton's intimate "The Pumpkin Eater" (1964) Sidney Lumet's prison camp drama "The Hill" (1965) and Martin Ritt's "The Spy Who Came in From the Cold" (1965; released in the United Kingdom in 1966).
In the mid-60s, Morris began to shoot musicals and won particular praise for his stunning camera work on Carol Reed's Oscar-winner "Oliver!" (1968), Herbert Ross' musicalization of "Goodbye, Mr. Chips" (1969), Ronald Neame's "Scrooge" (1970) and particularly Norman Jewison's "Fiddler on the Roof" (1971). The latter earned Morris the Best Cinematography Oscar. His sole television credit is Dan Curtis' evocative small screen remake of "Dracula" (CBS, 1974). As his career wound down, Morris worked again with Ross on the pastiche "The Seven Per-Cent Solution" (1976) and on three more films with Sidney Lumet, the stark "Equus" (1977), the colorful "The Wiz" (1978) and "Just Tell Me What You Want" (1980). Morris ended his career with two children's films, Jim Henson's "The Great Muppet Caper" (1981) and Henson and Frank Oz's "The Dark Crystal" (1982).