He acted in two adaptations of A. J. Cronin's novels, The Citadel (1938) and The Stars Look Down (1940), in addition to appearing in The Lady Vanishes (1938) and Under Capricorn (1949), both of the later films were directed by Alfred Hitchcock. Other roles were in Storm in a Teacup (1937), 23 Paces to Baker Street (1956), Dangerous Moonlight (1941), Swiss Family Robinson (1960), and I Was Monty's Double (1958), as well as the comedies A French Mistress (1960), The Ladykillers (1955), The Man in the White Suit (1951), The Court Jester (1955) (in which he played an evil, usurping king of England), Indiscreet (1958) and I Believe in You (1952). Parker was also the original Charles Condomine in the West End production of Noël Coward's Blithe Spirit.