Thank you Helig for your suggestions. The rank (private) and the unit (RGA) are recorded on the Llandudno Roll of Honour which preceded the War Memorial. A copy hangs at the back of Holy Trinity Church and I understand there may be other copies, including the Archive at Lloyd Street. The problem is that the rank of private is not reconcilable with the Royal Garrison Artillery where the equivalent rank would have been gunner or, possibly, driver – as I understand it.
Notwithstanding this, there does not appear to be a gunner or driver in the RGA that fits the criteria.
I have discovered a private in the Royal Welsh Fusiliers – 36032 – who joined in September 1915 and who was born at Denbigh. Unfortunately, even though his service record survives, I can find no link with Llandudno. He seems to have settled at Saltney near Chester. He died of heart failure at Litherland in 1916.
To be honest, I cannot be too hopeful about William Davies. He is one of the four names that I cannot trace. I keep returning to them every few months but without joy. I will be appending the other three names to this site shortly.