Cox was born in Banbridge, County Down, Northern Ireland, in April 1934.
He made his theatrical debut in Belfast during the mid-1950s, appearing in a production of A View from the Bridge by Arthur Miller.
His first appearance on stage in Dublin was as Ordulto in the play, The Masquerade of Henry IV in 1955.
In 1978 he played Sir Jasper Addleton in the Wodehouse Playhouse episode 'The Smile that Wins'.
During the 1980s, Cox's profile on television was raised after portraying Inspector Marriott in the drama Agatha Christie's Partners in Crime, as well as starring in Yes Minister as George, the driver of cabinet minister Jim Hacker.