William Morgan was one of the club’s founding members. Having been an original St Sidwell’s United player in 1901, he appeared in the first game played by Exeter City in 1904 and was captain during the reconstituted club's first two seasons. 

Previously a player for Exeter Wesleyan United, he became a member of the new St Sidwell’s United that was built around a group of 16- and 17-year olds who had attended St Sidwell’s school and lived close to the current St James’ Park. Recorded as scoring in the new club’s opening league match against Exeter YMCA on 5 October 1901,he was a regular member of the team during the following three seasons.

With St Sidwell’s being renamed Exeter City in 1904, he remained on the scene, became captain and featured in the opening league fixture against 110 Battery Royal Artillery on 10 September 1904. Appearing in all fourteen of Exeter City's league matches during 1904/05, he played ten games in the following campaign but only two in 1906/07.   

William Morgan, a butcher living on Sidwell Street in Exeter, is recorded in the 1901 census aged eighteen.