Peacock began his television and film career in the 1950s, becoming more active by the 1970s. Much of it consisted of televised classics, from William Shakespeare (including the title role in Titus Andronicus) to Sophocles, as well as Quilp in The Old Curiosity Shop. However, he also cropped up in comedy shows and years later was a regular on The Vicar of Dibley as parishioner Jim Trott. TV appearances include Highlander, The Bill, Waking the Dead, EastEnders, Last of the Summer Wine, Maigret, and Kingdom.
Film credits include Mel Gibson's Hamlet (as the gravedigger), Fred Claus (as Papa Claus), Catch Me a Spy, and Quartet (with Billy Connolly and Michael Gambon). Apart from acting, Peacock also wrote several pop songs in the 1960s, contributed scripts to television and radio variety series, and co-wrote most episodes of the sitcom The Sky Larks.