Sharp was born in Hobart, Tasmania, in 1921, according to official military records and his own claims, even though reference sources cite 1922 as his year of birth. He attended St Virgil's College and began appearing regularly in theatre productions at the Playhouse in Hobart.

He enlisted in the Royal Australian Air Force on 7 April 1941 and was transferred to Singapore. In addition to his military duties, he appeared in the radio and on stage but was invalided out before the city fell to the Japanese. He went on to act in Melbourne and Hobart and was discharged on 17 March 1944 at the rank of corporal.

After the war Sharp worked as an actor on stage and radio throughout Australia and in Japan, primarily in Melbourne. He then moved to England where he produced and co-wrote a film, Ha'penny Breeze (1950). He continued to act in small roles in such films as The Planter's Wife (1952) and The Cruel Sea (1953). He also played the character Stephen "Mitch" Mitchell in the 1953 British science fiction radio series, Journey into Space, but began to turn increasingly to writing and directing.

Sharp directed the first British rock 'n' roll movie, The Golden Disc (1958), released a year before the Cliff Richard vehicle Expresso Bongo (1959) and a full two years ahead of Beat Girl (1960). In Psychomania (1971), Sharp creates a visual fugue by riffing on the great themes of the counter-culture era: bikers, standing stones and ritual magic.

Among his other credits is Curse of the Fly, the spy-comedy Our Man in Marrakesh (1966), the fantasy Jules Verne's Rocket to the Moon (1967) and the 1978 remake of The Thirty Nine Steps, starring Robert Powell. He made another foray into spy culture with his feature-length reprise of the gritty Cold War TV drama, Callan (1974) starring Edward Woodward.

In 1975 Sharp worked on producer Harry Saltzman's abandoned pet project The Micronauts, a "shrunken man" epic to have starred Gregory Peck and Lee Remick.

Sharp died on 14 December 2011, after a short spell in hospital. He was survived by his wife Mary Steele, two sons and a daughter. Another son, Massive Attack producer, Jonny Dollar, predeceased him.

He was previously married to an Australian actress, Gwenda Wilson.

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