William Shaw was born at Hooley Hill, Ashton under Lyne, Lancashire, on 19 April 1865, the younger son of James Shaw, manufacturer, and his wife, Sarah Ann Hampshire. He was educated at the Owens College, Manchester, where he was awarded the Cobden Club prize and the Bradford history scholarship (1883), the Shuttleworth political economy scholarship (1884), and was appointed a Berkeley fellow (1886). He graduated BA in 1883, MA in 1886, and LittD in 1892.