Wilmer made his theatre stage debut in 1945 in repertory at Rugby. He appeared frequently on the London stage, mainly in classical and Shakespearean roles. He made his first major film appearance in Laurence Olivier's "Richard III" (1955); thereafter, he appeared in a large number of films, mostly in supporting roles. They include several epic films: as M. Desmoulins in "The Battle of the River Plate" (1956), as Al-Mu'tamin in "El Cid" (1961), "Cleopatra" (1963), "The Fall of the Roman Empire" (1964), as Khalifa Abdullah in "Khartoum" (1966), as Maj. Gen. Francis de Guingand in "Patton" (1970), as Sir Thomas Fairfax in "Cromwell" (1970), and "Antony and Cleopatra" (1972). Other appearances include "Jason and the Argonauts" (1963) as Pelias, the Pink Panther films "A Shot in the Dark" (1964) and "Revenge of the Pink Panther" (1978), "The Vampire Lovers" (1970), "The Golden Voyage of Sinbad" (1974), and "Octopussy" (1983).