|This article does not cite any references or sources. (November 2007)|
Wragge joined Wolverhampton Wanderers in 1919, but left to join Oakengates Town without making his league debut. He rejoined Wolves in 1921, but again left for Oakengate having failed to make a first team appearance.
He joined Bristol Rovers and finally made his league debut in the 1923-24 season. Over two seasons, he made 62 league appearances before moving to non-league Stafford Rangers. In 1927 he joined newly promoted Torquay United, playing in Torquay's first ever game in the Football League, a 1-1 draw at home to local rivals Exeter City on 27 August. He played 27 times that season before moving on to Walsall in 1928.
He made just two league appearances for Walsall before leaving league football, joining Madeley Miners Welfare.