Movies:
* The Elephant Man (1980) - as the Doctor
* The Bounty (1984) - as Dr. Monkhouse
* The Missionary (1986) - as Dr. Harris
* The Madness of King George (1994) - as Dr. Willis
* The Adventures of Baron Munchausen (1988) - as The King
* Shakespeare in Love (1998) - as Lord Hunsdon
* Gosford Park (2001) - as Mr. Meredith
* The Importance of Being Earnest (2002) - as Mr. Cardew
* The King's Speech (2010) - as Lord Stamfordham
Television:
* The Avengers (1961-1969) - in multiple episodes
* The Saint (1962-1969) - in multiple episodes
* Doctor Who (1963-present) - as The Master in the episode "Frontier in Space"
* The Persuaders! (1971-1972) - in multiple episodes
* Upstairs, Downstairs (1971-1975) - as Lord Bellamy
* The Pallisers (1974) - as Plantagenet Palliser
* The Duchess of Duke Street (1976-1977) - as Lord Kilmartin
* The Jewel in the Crown (1984) - as Mr. Layton
* The House of Cards (1990) - as the Bishop of Truro
* Inspector Morse (1987-1993) - in multiple episodes
* The Bill (1984-2010) - in multiple episodes
* Midsomer Murders (1997-present) - in multiple episodes
* Heartbeat (1992-2010) - in multiple episodes
* Casualty (1986-present) - in multiple episodes
* Holby City (1999-present) - in multiple episodes
This is not an exhaustive list, but it highlights some of his most famous and significant roles.
It is worth noting that William Gaunt has been a prolific character actor, often playing authoritative figures like doctors, politicians, and clergymen. He has also appeared in many popular British television series over the years. His long career has been a testament to his acting talent and his dedication to the craft.