William Bradshaw was the son of Woolwich Arsenal manager, Harry.
The forward spent four years at the Manor Ground after joining as an amateur in March 1900, signing professional terms four months later.
Bradshaw made a goalscoring senior debut in a 2-1 win over Blackpool in November 1902 after a successful period in the second string, where he scored 39 goals in 66 appearances.
He played three times the following campaign, netting once more before transferring to Fulham in summer 1904.
Bradshaw's brother, Joseph, also played for the reserves.
He later played for Burton United and Ton Petre (Wales) before moving to Canada.