Margaret Allison states that his parents lived at Radcliffe and was aged 21 years when he died.
Soldiers Died in the Great War states that he was born at Bamburgh and enlisted at Radcliff, Lancs, but this could easily have been Radcliffe, Northumberland.
There are three "William Smiths" remembered in Ashington on A17.01 (A17.27)A17.43
However, there is only one "W. Smith" or "William Smith" on A17.06 A17.08 A17.11 so without more information it is difficult to tell which man is being remembered.