In 1956 Godfrey joined the Radio Drama Company by winning the Carlton Hobbs Bursary. He made his film debut in Miss Julie (1972), and appeared in several British films of the 1980s, 1990s and 2000s, including A Room with a View, The Remains of the Day, The Importance of Being Earnest, The Count of Monte Cristo, Dimensions and Les Misérables. He also played Leonardo da Vinci in the Cinderella adaptation Ever After alongside Drew Barrymore and Dougray Scott. He had many roles on television, appearing in Doctor Who, Inspector Morse, and other series.
