Leigh, Lancashire born right half Billy Morgan began his football career with Horwich in 1895 before joining Second Division Newton Heath (Manchester United) in January 1897, making his Football League debut against Darwen in March 1897. Initially mainly a fringe player, he broke into the first team on a regular basis from the start of the 1898-99 season, and had 4 seasons as an automatic inclusion in the Newton Heath line-up before losing his place and joining Bolton Wanderers in March 1903 after 7 goals in 152 appearances. His brief stay at Burnden Park encompassed 3 appearances as Bolton were relegated, and he was released, joining Southern League Watford in July 1903.
His one Watford season, in which Billy Morgan played in every first-team game and scored twelve times from the penalty spot in all competitions (a club record), brought the Southern League Second Division Championship to Cassio Road. Of those 10 goals in 22 appearances came in Southern League and FA Cup games. In May 1904 he returned to the Football League with Leicester Fosse, scoring 12 goals in 73 appearances for The Fossils before returning to The Southern League with New Brompton (now Gillingham) in August 1906. He joined Kidderminster Harriers in 1909 and Newton Heath Athletic in March 1910 before finishing his career with Goole, whom he joined in November 1911.