Hedley was born in London and educated at Emanuel School. His screen career began in 1950 with a 13-minute drama-documentary about polio called A Life to be Lived. In the 1950s he made a number of appearances in films and on television, such as Left Right and Centre, Fair Game and the Alun Owen-scripted No Trams to Lime Street with Billie Whitelaw.

He appeared in a number of British films of the 1960s, including Lawrence of Arabia (1962), The Scarlet Blade (1963), Witchcraft (1964), Of Human Bondage (1964), The Secret of Blood Island (1964) and The Anniversary (1968). He also had a lead role as Lt. Colonel Preston in Colditz (1972–74).

His other TV appearances include: The Saint (1965), Gideon's Way ("The Alibi Man", 1965), Softly, Softly (1967), Dixon of Dock Green (1969), The Buccaneers (1957), the ex-serviceman Alan Haldane in Who Pays the Ferryman? (1977), Return of the Saint (1979), One by One (1984), Remington Steele (also 1984), Only Fools and Horses ("A Royal Flush", 1986), 'Allo 'Allo (1992), Dalziel and Pascoe (1998) and the TV film version of Brief Encounter (1974).

Hedley later appeared in the James Bond film For Your Eyes Only (1981) as Sir Timothy Havelock, also voicing Havelock's parrot. Soon after this, in the autumn of 1981 he played the lead role (cynical investigative cop Fred Williams) in Lucio Fulci's The New York Ripper (Lo squartatore di New York, 1982), in which his voice was dubbed. He also starred with Stanley Baker and Jean Seberg in the film of Irwin Shaw's In The French Style (1963).