He trained at the Royal Academy of Dramatic Art. He entered repertory at the David Garrick Theatre, Lichfield, Staffordshire for two years and appeared in early British television plays. Jeffries built a successful career in British films mainly in comic character roles and as he was prematurely bald he often played characters older than himself, such as the role of father to Caractacus Potts (played by Dick Van Dyke) in the film Chitty Chitty Bang Bang (1968), although Jeffries was actually six months younger than Van Dyke. His acting career reached a peak in the 1960s with leading roles in other films like Two-Way Stretch (1960), The Trials of Oscar Wilde (1960), Murder Ahoy! (opposite Margaret Rutherford), First Men in the Moon (1964) and Camelot (1967).