Denham had made an early foray in films in 1941 in a bit part in "Barnacle Bill" but did not come to the medium in earnest until 1947 when he appeared in a small role in "Daybreak" and played the uppercrust Major Frazer in "Blanche Fury", a film based on a real-life murder case. These films set a standard for Denham's roles, often cast as uppercrust sometimes stolid domestic workers, but always 'veddy, veddy English'. Later, he often played working stiffs, such as his small role as the trawler skipper in "Those Magnificent Men in Their Flying Machines" (1965) and an undertaker in "Julia" (1977). Virtually all his films were British productions, with exceptions like "23 Paces to Baker Street" (1956) and "Midas Run" (1969). Still working into his 80s, Denham portrayed George Martin, the aged bachelor bookstore clerk, warmed by the letters sent by Helen Hanft (Anne Bancroft) in "84 Charing Cross Road" (1987).
Denham's small screen work has been frequent, but rarely provided him with leading roles. An exception was "From a Far Country: Pope John Paul II" (NBC, 1981), in which he had the title role. (The movie also had a theatrical run in Europe.) He played another priest in the British TV production "The Potting Seed", one of the first dramas shown on the CBS Cable channel during its short life in 1981. Denham also was cast as Senor Diego alongside Alec Guinness and Leo McKern in "Mongsignor Quixote" (PBS, 1987). One of his last roles was in the Harlequin Romance "Tears in the Rain" (Showtime, 1988).