Whitwick, Leicestershire born inside right Teddy Glennon joined Second Division Grimsby Town from Kilnhurst Town in November 1907, making his Football League debut against Bradford City the same December. However, initially playing right half, he only made 10 appearances over two seasons for The Mariners before moving to Midland League club Denaby United in the 1909 close season. Converted to the forward line, he then signed for First Division club Sheffield Wednesday for £175 in the summer of 1910 making his debut for The Owls at Oldham Athletic on Christmas Eve.
He soon became a regular performer and frequent scorer for Wednesday, scoring 42 goals in 133 matches until the suspension of football due to the onset of the First World War in May 1915, and during the War he played wartime league football for The Owls through to their 1918-19 campaign. After the War he joined Second Division club Rotherham County in July 1919, playing the first two seasons of post-war League football, and missing only two matches in 1919-20, scoring 17 goals in 66 appearances for County, before joining non league Rotherham Town in 1921.
Glennon was also an excellent cricketer and played twice for Leicestershire in 1921. In his two first class matches he scored twelve runs with a highest score of 7.