Dunning joined the Royal Navy aged 18, and served for two years. He later managed a newsagent's shop and was also a window cleaner. Having been Yorkshire amateur champion on eleven occasions, and the CIU Championship in 1963, 1966 and 1969, Dunning turned professional in 1971 at the age of 45. He played his first World Championship match in 1972, when he lost to John Pulman in the first round, after beating Pat Houlihan and Graham Miles in qualifying. He produced his best performance in 1974, when he reached the quarter-final, subsequently losing his match against Miles 13–15. Dunning's final appearance in the main stages of the event came in 1982.