Hi David, thanks for the kind offer.
Yes, I see Constance Mary Moore, mother Catherine Moore c.17 SEP 1871 Santon in the IGI now. Perhaps if someone has access to the Santon baptism register film they might be kind enough to check if the father is mentioned? Though I suspect if he was he might have appeared in the Index even if the daughter wasn't listed under his name.
As Constance was married to Albert Pickard under the name of Clague in August 1889, I wonder if her marriage certificate would give her actual, presumably Clague, father's name, or the name of her mother's husband, if you see what I mean?