Swift was active in television, stage, and radio since the 1960s. He appeared on such dramatic series as The Avengers (in the Diana Rigg era) and The New Avengers, Father Brown, Poirot, Day of the Triffids, and Bergerac. Swift was a familiar face in costume drama and period pieces, including the 1972 War and Peace miniseries (as Napoleon Bonaparte), the 1984 miniseries Freud (as Freud's colleague Josef Breuer), and the 1988 Jack the Ripper TV movie (with Michael Caine). In 1981, he seemed to specialize in Germans, from Teutonic professors in the miniseries Private Schulz and Winston Churchill: The Wilderness Years to General Rattenhuber in the TV movie The Bunker.