Cundy's furthest progression in an event in his début season was in the 1991 UK Championship, where he reached the last 64, beating Jason Curtis 6–2, Peter Bardsley 6–2, Darren Guest 6–1, the young Anthony Hamilton 6–3, Graham Cripsey 6–5, Gary Natale 6–4 and Jim Wych 6–2, before losing 2–9 to Mark Bennett.

[1] Cundy entered thirteen tournaments during his second season as a professional; again, his furthest run was to the last 64, this time in Event Three of the 1993 Strachan Challenge, where he lost 1–5 to future World Championship finalist Nigel Bond.

Cundy began the 1994/95 season with a ranking of 138th, and reached the last 32 of the 1995 Welsh Open, defeating Adrian Gunnell 5–0, Jason Greaves 5–2, Mark Davis 5–1, Roger Garrett 5–0, Nick Terry 5–4 and former world number two Tony Knowles 5–1 before eventually losing 3–5 to Antony Bolsover.

Having retained his professional status as the world number 103, Cundy was unable to replicate his good form of the last few seasons in 1996/1997, earning only £490 from reaching the last 96 of the 1997 Welsh Open, where he lost 3–5 to Euan Henderson.

He regained his place for the 2006/2007 season, but won only two matches in ranking events - 3–2 over Ian Preece in the 2006 Grand Prix, and 9–6 over Mark Joyce in the 2006 UK Championship - and resumed his amateur career thereafter.