Returning to the UK in 1953, Allen made his film debut in Alfred Hitchcock's Dial M for Murder (1954). He gained experience as a local radio broadcaster and appeared on television in plays and documentaries, before returning to Britain.
After his parents returned to Britain, he was evacuated to Canada during the Second World War where he remained to finish his education at McGill University in Montreal. Allen was born in Nyasaland (now Malawi), where his father was a tobacco farmer.