Arnold, Nottinghamshire born inside forward Bob Dennison signed for Norwich City from his local club Arnold St Mary’s in 1920, playing 26 games in their inaugural League season having made his Football League debut against Crystal Palace in September 1920. Playing mainly at inside right, he was the club’s top scorer with 14 goals in 1922-23, including a hat-trick in a 3-2 win over Millwall in April 1923, and over four seasons in East Anglia he scored 38 goals in 126 games.
A move to Brighton & Hove Albion followed in the summer of 1924, and he scored on his Brighton debut in a win at Brentford that August and then a hat-trick once again against Millwall in the next match, this time in a 3-3 draw. His haul of 13 goals in 28 games for The Seagulls was enough to persuade First Division Manchester City to sign him. He got into the side in November and started well scoring 3 goals in his first 4 games but the goals tailed away, City were relegated, and after 4 goals in 10 games he was sold to Second Division club Clapton Orient the next summer.
Playing mainly at inside left, Dennison top scored, one ahead of Donald Cock, in his debut season with 15 goals, and enjoyed three good seasons in East London, scoring 31 goals in 76 appearances but when they too were relegated in 1929, Dennison was off-loaded to Chesterfield. He played a final Football League season at Saltergate scoring 7 goals in 31 games for The Spireites before joining non league Yarmouth Town in 1930.