Gwynn is perhaps best remembered for his role in the first episode of the BBC comedy Fawlty Towers "A Touch of Class" (1975) as the conman "Lord" Melbury who eventually humiliates Basil Fawlty. For Hammer Films, he performed in several productions including the war film The Camp on Blood Island (1958), and Never Take Sweets from a Stranger (1960), a rare drama film for the studio; the actor also appeared in one of their very best horror movies, The Revenge of Frankenstein (1958), in which he played a tragic experimental subject who turns into a cannibalistic killer, and the less well-regarded Scars of Dracula (1970) in the role of a priest determined to battle Count Dracula.

Gwynn also appeared on several adaptations of plays on the Caedmon Records label. Among them were Cyrano de Bergerac, in which he played Le Bret, and Julius Caesar, in which he played Casca. Both productions starred Ralph Richardson in the title roles. Gwynn also appeared in a BBC serialised adaptation of Great Expectations as Joe Gargery in 1959. Gwynn died on 29 January 1976 in London from a heart attack, aged 59.