There were minor variations to the standard Gunner cap badge similar to the one you cite involving the scroll beneath the crown and that beneath the gun but the basis composition and outline of all remained the same. The pattern was established in 1902, well before the Great War.
Samuel's badge does resemble the RA badge, the shadows making it look different, and he could be in the RHA although one would need his shoulder titles to know for sure.
Medal cards can often add to confusion as the RFA and RHA were administered from one office called RH and RFA Records and a man's branch is not always faithfully recorded.
All that said, the task would be much as you describe, trawling through all artillerymen called Samuel Iles or S Iles etc etc and hoping to find one with biographical details. (Except I find none).
Another approach - there are 10 medal cards listed on the National Archives site for men called Samuel Iles. Checking each of the cap badges (none Royal Artillery), the Army Cyclist Corps has a Samuel W Iles and the badge could be that seen in the pic.
Another thought - given that 60% or so of records were lost in WW2 to bombing and a man who did not serve overseas did not get medals hence no card, he may be in the unknown unknowns category.
Does the birth cert have a note of the father's regiment? Is there an absent voters' list for the area where he lived? Did he have a second forename?
MaxD
