Well, being an Old Contemptible, there should most certainly be a medal card for him, and we're looking for someone who was awarded the 1914 Star.
So how many possible matches are there (all Middlesex Regt, and eliminating any with the wrong middle initial)?
2725 Pte Charles Clarke
PW/3758 Pte Charles Clarke
6386 Pte Charles Clarke
3632 Pte Charles Clarke
525 Pte Charles Clarke
G/5753 Pte Charles H Clarke
And that would seem to be it for the shortlist. It might be tempting to go with the last one with the middle initial H, but things are never that simple.

Let me see if I can eliminate any of the six.