There is an Army Pension record for Edmund Mellor bc.1888 Darlington who enlisted on 2/9/1914 in 10th K.R.R.C. which is clearly your man as refers to wife Gertrude Harrold (married Register Office, Aston 17/1/1909), plus the 3 children he had at that time. However, the record goes on to state he was discharged on 20/10/1914 due to 'defective eyesight' which would suggest that he didn't take part in the war after all.
Did he therefore re-enlist later into the Worcester Regiment or is that medal record for another Edmund Mellor?
So, both army record plus 1911 census state he was born in Darlington.
There are some confusing trees on Ancestry (in that some contradict each other) regarding him the main consensus being he was the John Edmund Williams birth June.1888 West Bromwich, Staffs.
1891 census showing:
William Mellor bc.1863 Cannock, Staffs.
Emma Mellor bc.1864 Monmouthshire
Jessica Mellor bc.1888 Burton on Trent
John E. Mellor bc.1888 Darlaston
Emma Mellor bc.1890
In 1894 William Mellor married an Annie Bosson Sept.1894 Stoke upon Trent.
It would appear that William and 'first' wife Emma were not actually married but as the 3 children shown in 1891 were all registered as Williams one would assume Emma's maiden name was Williams.
So, one could argue that 'Darlaston' was misheard when he enlisted and recorded as Darlington BUT since Edmund himself filled out 1911 census form and entered 'Darlington' that doesn't pan out.
I think you definitely need to get a copy of his 1909 marriage certificate to confirm if his father was indeed the William referred to above. None of the trees I looked at seemed to have any real 'proof' and don't know if their recorded findings are pure conjecture or not. I, personally, wouldn't want to go down this 'route' without some further evidence, the marriage certificate being the first port of call.
Annette