Godfrey made his film debut as a different bus conductor, in the 1949 Ealing Studios comedy Passport to Pimlico. Similar roles followed, in films such as The Flaw, Work Is a 4-Letter Word (with David Warner), Ring of Bright Water, The Adventures of Sherlock Holmes' Smarter Brother (with Gene Wilder, Madeline Kahn, and Marty Feldman), and the seventies horror anthologies The Vault of Horror and From Beyond the Grave.
Godfrey was busier on television, as an array of cab drivers, landlords, workmen, or just men in pubs. He had running parts on the sitcoms On the House (1970-1971, as building crew member Arnold), Love Thy Neighbour (1972-1976, as factory worker Arthur), and Mind Your Language (1978-1979, as janitor Sid). He made episodic appearances on The Avengers, The Saint, Til Death Us Do Part, On the Buses (as yet another bus conductor), Steptoe and Son, Z Cars, Doomwatch, and Chance in a Million (with Brenda Blethyn).