Margaret Allison states that he lived at Hirst, Ashington.
Soldiers Died in the Great War states that he was born at Hirst and enlisted at Ashington.
There are three "William Smiths" remembered in Ashington on A17.01 (A17.27) and A17.43
However, there is only one "W. Smith" or "William Smith" on A17.06, A17.08 and A17.11 so without more information it is difficult to tell which man is being remembered.