Those are good finds Dave and DownUnder. If the William Davies is Hugh's Grandfather and if William was illegitimate as Hugh thinks then it is possible that Dorothy (age not mentioned) could be William's mother.
The Baptism records may help but I'm not sure if Llansanffraid Glan Conwy's records are at the Conwy Archives. Although Glan Conwy is now in the County of Conwy I know some of the Parish records are elsewhere. I'll have a look when I'm there next.
Anyway, here's a photo taken today of 7 Alexandra Road Llandudno where William once lived. ( No 7 is the door on the right)
I have joined FindMyPast for 1 month and have been pouring over many, many records to a) make sure I have the correct 1901 Census record for William Davies, and to explore a number of other possibilities. For confirmation of the 1901 Census record, I used 1876 +/- 1yr as the birth date (based on 1911 Census/Marriage Certificate/my father's Birth Certificate), Denbighshire as the Birth County, and Marital Status as Single applied to the 1901 English, Wales and Scotland Census. Of the 19 names listed (without a middle initial) the Llandudno entry is the only one to tick the majority of boxes (although it was more about eliminating the other 18 entries).
Having confirmed what I think is the only logical match for the 1901 Census, I decided to look at the 1891 Census records using 1876 +/- 1yr as the birth date (based on 1911 Census/Marriage Certificate/my father's Birth Certificate/1901 Census), Denbighshire as the Birth County, and Marital Status as Single applied to the 1891 English, Wales and Scotland Census. A total of 17 names were listed (without a middle initial). Only one of the entries looked positive - Birth Place Glan Conway, Occupation - Shoe Maker and even included the Father. However, when I checked on this family for 1901, William Davies was listed as still living there. All other entries listed birth towns other than Glan Conway or Llansaintffraid in Denbigshire or listed a father. All in all, nothing positive.
I had previously, around 6 months ago, flagged the possibility of Dorothy being William's mother. I traced this family from 1841 to 1881. Edward and Margaret had 10 children during this period, 7 of them females, anyone of them potentially the mother of William Davies. Intriguingly, Dorothy (4) was listed in the 1861 Census but absent from the 1871 Census, only to reappear in the 1881 Census (23) with a William Davies. Will try to find an entry for Dorothy in the 1871 Census but not feeling too confident.
My apologies for delays in thanking you all or providing input. I suffer from Chronic Fatigue Syndrome and have been particularly out of sorts in the past few weeks.