Margaret Allison states that he enlisted in Alnwick and was aged 23 years when he died.
Soldiers Died in the Great War states that he was born in Warkworth.
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.