During the Second World War, he served as a FLIGHT lieutenant with the RAAF from 6 December 1941 to 1 July 1947, including Service with 111 Air Sea Rescue FLIGHT.

Cuthbertson arrived in Britain in 1947, and appeared shortly thereafter as Romeo in Romeo and Juliet at the Boltons. In London's West End, he appeared as Laertes in Hamlet, Aimwell in The Beaux Stratagem, and Octavius Robinson in Man and Superman, among many other roles.

He was often cast in military roles, which was quite Common in actors of his generation, especially those with a military air about them. He was Captain Eric Simpson in Tunes of Glory (1960) as well as being cast as more stuffy regimental types in such films as The Guns of Navarone (1961) and Carrington V.C. (1955), which also starred David Niven. He also made a brief appearance as a harassed staff officer, who then gets blown up, at the beginning of Ice Cold in Alex (1958). In 1962 he played a school Teacher in Term of Trial with Laurence Olivier. He appeared four times in the television series The Avengers.

Perhaps surprisingly Cuthbertson also had a talent for playing comedy, which led to his best known role, although again playing a mustachioed military character, as Colonel Hall in the "Gourmet Night" episode of the hit sitcom Fawlty Towers in 1975. He appeared in many roles on British television, including with Tommy Cooper, Dick Emery and Frankie Howerd, and in All Gas and Gaiters, Danger Man, UFO (1970 episode "The Square Triangle") and Terry and June, where he played annoying neighbour Tarquin Spry. He was a regular guest on The Morecambe & Wise Show from 1973 to 1976. One of his last TV appearances was in Michael Palin's East of Ipswich in 1987.

One of his last stage roles was in The Corn Is Green by Emlyn Williams at the Old Vic in 1985.