Williams refereed the most World Snooker Championship finals of any referee, his first at the Crucible Theatre being the 1978 final between Ray Reardon and Perrie Mans. Having previously refereed the last session of the 1976 final, Williams took charge of eight other finals at the venue until 2002, including all three that went to a . He refereed the most viewed snooker match in history, the 1985 World Snooker Championship final between Steve Davis and Dennis Taylor where Taylor won on the final in the deciding frame. He was also the referee during Cliff Thorburn's maximum break against Terry Griffiths in 1983, the first maximum in the history of the competition.