Morse made his film debut in the 1942 comedy The Goose Steps Out starring Will Hay and continued with roles in Thunder Rock, When We Are Married and This Man is Mine (released as A Soldier for Christmas in North America) with Glynis Johns and Nova Pilbeam. Other notable films include Kings of the Sun with Yul Brynner, Justine, and Puzzle of a Downfall Child with Faye Dunaway. He also appeared in the thrillers Asylum (1972) with Peter Cushing, Funeral Home with Kay Hawtrey and Lesleh Donaldson, (1980), and The Changeling with George C. Scott (1980). He worked on several Lacewood animated productions, notably as the voice of Dragon in The Railway Dragon, alongside Tracey Moore who played Emily. In 1999 he filmed the dramatic comedy Taxman with Billy Zane, released as Promise Her Anything and on DVD as Nothing to Declare. His final film appearance was in I Really Hate My Job, released in 2007.