William Parker was born in Liverpool on 27th May 1915. A left-back, he joined Hull City in 1937. He played 30 games for the club before being signed by Major Frank Buckley, the manager of Wolverhampton Wanderers in 1938. He joined a squad that included Stan Cullis, Gordon Clayton, Bill Morris, Dennis Westcott, George Ashall, Alex Scott, Jack Taylor, Tom Galley, Dicky Dorsett, Bryn Jones, Joe Gardiner and Teddy Maguire.

In the 1938-39 season Wolves finished second to Everton. However, Parker only played in three games and he left the club at the end of the season.

William Parker died in 1980.