Subsequent roles included a theatre manager opposite Laurence Olivier in the film version of The Entertainer and a policeman in Michael Powell's Peeping Tom (both 1960).

He made an impression as Thomas Howard, 3rd Duke of Norfolk in A Man for All Seasons (1966),[9] co-starred with Michael Caine in the war movie Play Dirty,[7] and had a major role as Lord Bothwell in Mary, Queen of Scots.

[6] During the production of Stanley Kubrick's 1968 film 2001: A Space Odyssey, Davenport read the lines of HAL 9000 off-camera during the computer's dialogues with actors Keir Dullea and Gary Lockwood.

[1] He appeared as Ebenezer Scrooge's grudging father Silas in the George C. Scott version of A Christmas Carol (1984), and played opposite Michael Caine again in the 1988 Sherlock Holmes spoof Without A Clue, which was Davenport's second-last feature film.

[12][6] According to Jerry Bruckheimer, producer of the Pirates of the Caribbean films, Jack was cast as the James Norrington character partly because of Nigel's involvement in A High Wind in Jamaica.