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. This remained Burke's best progression at the World Championship.