Update Re William Henry Edward Wilkinson:
Following your helpful detective work I have since obtained my grandfather's birth certificate and am able to confirm that he was indeed William Henry Edward Wilkinson b.18.1.1887 in Kennington. The birth certificate confirmed his father as Henry Richard Wilkinson and his mother as Clara Jane Mostran. So thank you all for your help.
I have since joined Ancestry and am gradually fleshing out the bones of my family but my grandfather still remains much of a mystery with little evidence of him beyond the age of 4 in the 1891 census, his marriage to my grandmother Lilian Maud Tabor on 5.8.1913., and a possible death in October 1962. My grandmother remarried in 1941 so if William was still alive they were either divorced or she committed bigamy.
This new photo has only just been discovered and is almost certainly of my grandfather holding my father as a baby (b.11.11.1914). It is one of just two photos and the only one of him as an adult. I recently posted it in the Common Room hoping that the uniform would provide some extra info...but unfortunately without a great deal of luck despite members' best efforts. He remains a mystery...but not quite the total mystery he was before your help!
Kind regards, Fred