Arthur Denny first showed promise as a teenager when he finished second in a one-lap handicap race in his home city of Bristol in 1902. A member of the Bristol Wheelers at the time, he joined Rover RCC in Birmingham in 1906 and it was not long before success came his way, as he was the NCU Birmingham Centre 25-mile champion in his first year with his new club. He won the Midland Centre one and 25-mile titles in 1907 and, the following year, regained his Birmingham Centre 25-mile title. Prior to the London Olympics, Denny raced mostly in the Midlands, but took to the mighty Herne Hill track in the months leading up to the Games and, after finishing second in the Southern Counties Championship, was selected for the Great Britain team.
A month after the Olympics, Denny represented England at the British Empire Championships at the Belfast Oval. In 1909 he was runner-up to [Bill Bailey] in the four-mile race at the NCU Championship at Portsmouth, and in 1910 was runner-up in both the NCU 25- and 50-mile championship races. In the longer distance, he lost to Charles Denny by half-a-wheel after around two hours and 20 minutes of racing, He narrowly missed out on the five-mile title in 1911, when finishing third behind [Victor Johnson] and [Clarrie Kingsbury].