Born Reginald Leigh Dugmore in Richmond, Surrey, England, he began his film career in 1915 and made films both in the US and England until the 1960's. He came from a theatrical family who came to the US in 1912 to appear in the stage production Quaker Girl. His father was the actor and singer W. H. Denny.
Denny was a well known actor in silent films and with the advent of Talkies he became a character actor. He played a lead role in a number of his earlier films, generally as a comedic Englishman, and later had reasonably steady work as a supporting actor in dozens of movies, including a screen version of Anna Karenina with Greta Garbo and the Frank Sinatra "caper" movie Assault on a Queen.
Later, Denny made frequent appearances in television during the 1950s and 60's. His last role was in Batman: The Movie (1966) as Commodore Schmidlapp.