Denison was born in Doncaster, West Riding of Yorkshire, in 1915. He was brought up by his aunt and uncle from the age of three weeks, following the death of his mother and his estrangement from his father.
Denison was educated at Wellesley House School, a Preparatory school in the coastal town of Broadstairs in Kent, followed by Harrow School in North West London, where he took part in school productions. It was while at Magdalen College, Oxford University, studying modern languages that he met John Gielgud and decided to take up acting seriously.
After graduating, Denison attended the Webber Douglas Academy of Dramatic Art, where he met Dulcie Gray, a fellow student, who later became his wife in 1939 and his acting partner. They appeared in more than 100 West End productions, together in some 28 plays in London and countless tours of Britain and elsewhere. They also appeared together in several films. Their intertwined professional lives reached their pinnacle in 1996 with their first appearance together on Broadway, in the Peter Hall production of Oscar Wilde's An Ideal Husband. Their last appearance together was in Curtain Up, an evening of reminiscences at the Jermyn Street Theatre in London, shortly before he died.
Denison made his stage debut in 1938 as Lord Fancourt Babberly in a Frinton-on-Sea production of Charley's Aunt and in the same year, he made his West End appearance at the Westminster Theatre, playing Paris in Troilus and Cressida. He made his film debut in the film Tilly of Bloomsbury in 1940.
During the Second World War, he interrupted his career to join the Royal Signals and then transferred to the Intelligence Corps and was involved in the liberation of Greece, He remained in the British Army until he was demobbed in 1946.
Denison's first film after the war was Hungry Hill (1947) in which he had a support role. He also supported in The Blind Goddess (1948) then was cast in the lead in My Brother Jonathan (1948). This was a big hit and saw Denison voted the sixth most popular British star of the year.
Denison appeared in a war film, Landfall (1949), and a romantic drama with his wife, The Glass Mountain (1949). In 1949 exhibitors voted him the eighth most popular British film star in the country.
Denison and his wife then made The Franchise Affair (1951). After a cameo in The Magic Box (1951), he and Grey were in Angels One Five (1952), one of the most popular movies of the year in Britain that year. Also popular was The Importance of Being Earnest (1952).
Denison and Gray were in There Was a Young Lady (1954), then he supported Richard Greene in Contraband Spain (1955). He began to work increasingly on television, taking the lead in the Associated-Rediffusion/ITV series Boyd Q.C., which ran for 78 episodes from 1957 to 1963. In films, Denison drifted into support roles with The Truth About Women (1957) and Faces in the Dark (1960).
While touring in Australia he and Gray made a TV play Village Wooing (1962).
Denison became the director of the New Shakespeare Company in 1971. He also served as council and vice-president of Equity.
He was the subject of This Is Your Life on two occasions, in February 1977 when he was surprised by Eamonn Andrews in the foyer of the Inn on the Park in London's Park Lane; and in April 1995, when Michael Aspel surprised him and his wife Dulcie Gray, on board the Sir Thomas More motorboat at Teddington Lock, for a joint tribute.
He published two volumes of memoirs, Overture and Beginners (1973) and Double Act (1985). He also contributed many entries to the Dictionary of National Biography. Denison was honoured by Queen Elizabeth II with the Silver Jubilee Medal in 1977 and both he and his wife were designated Commanders of the Order of the British Empire (CBE) in 1983.
His final film was Shadowlands (1993). He and Gray had a hit on Broadway in a revival of An Ideal Husband in 1996–97 which ran for over 300 performances.
His last stage appearance was Curtain Up with his wife.
He died of cancer in Amersham, Buckinghamshire, in 1998, aged 82.