Denham was born in Beckenham, Kent, the son of Eleanor Winifred (née Lillico) and Norman Denham. He was educated at Tonbridge School and trained as a lift engineer. Denham eventually became an actor in 1934 and appeared in live television broadcasts as early as 1938, continuing to perform in that medium until 1997. Like fellow actor James Robertson Justice he played amateur rugby for Beckenham RFC. He was awarded the OBE in 1992.