Born in London, Dempster began his screen career in the silent film era. His credits included Vice Versa, Anna Karenina, The Winslow Boy, The Fan, Scrooge, The House Across the Lake, and The Ghost Train.
Thirty-six years separated Dempster's first and last appearances on Broadway. He debuted in the 1929 melodrama Rope's End by Patrick Hamilton and in 1965 replaced Peter Sallis as Dr. Watson in the Sherlock Holmes-inspired musical Baker Street.
Dempster died in Chicago, Illinois.
- The Great Well (1924)
- Lord Babs (1932)
- Music Hath Charms (1935)
- Crackerjack (1938)
- Marigold (1938)
- Three Silent Men (1940)