Williams reached the semi-final of the World Snooker Championship three times, losing to John Spencer in 1969, in 1972 to Alex Higgins 30–31 (having been four frames ahead with five left to play) and, in 1974, 7–15 to Graham Miles. He never won a World Championship match at the Crucible Theatre after it became the World Snooker Championship's venue in 1977, despite playing at the venue on eight occasions (a record he shares with Cliff Wilson). He recovered from 8–2 down to win 9–8 against Terry Griffiths in the first round of the 1978 UK Championship, in the future World Champion Griffiths' first match as a professional. Williams was the 1973 Pot Black runner-up, losing 33–99 to Charlton in the one-frame final.