Williams became a lecturer at the University of Edinburgh in 1962, eventually becoming a reader in 1972, then a professor ten years later, where he held the first chair in performance practice in the UK.
He was made Distinguished Professor of Arts and Sciences at Duke University in Durham, North Carolina in 1985.
Here, he was also chairman of the music department (1985–1988), university organist (1985–1990), and the director of the graduate center for performance practice studies (1990–1997).
He was a professor at Cardiff University from 1996 to 2002, and served as chairman, subsequently President, of the British Institute of Organ Studies from 1996 to 2002.
[2] It was here where Williams suggested that the famous Toccata and Fugue in D minor, BWV 565 was probably not written for the organ, and possibly not by Bach.