[3] He reached the semi-finals of the 1974 World Amateur Snooker Championship,[4] and was invited to participate in the 1974 Norwich Union Open, where he lost 2-5 to Ray Reardon, the reigning professional World Snooker Champion.
[5] Burke was accepted as a member by the World Professional Billiards and Snooker Association (WPBSA) in 1982.
[1][6] He also lost in the first match of his third and final tournament of his first season, defeated 9–10 by Paddy Morgan in the qualifying round of the 1983 World Snooker Championship.
[1] He started the 1983–84 snooker season with a 2–5 loss to Geoff Foulds in the qualifying for the 1983 International Open, but then defeated Foulds 5-4 in qualifying for the 1983 Professional Players Tournament, before losing 3–5 to Joe Johnson.
In the qualifying rounds of the 1984 World Snooker Championship he eliminated Billy Kelly 10-7 and Bob Harris 10-4 but was then knocked out 10–5 by Mike Hallett.