If there had only been half a dozen names, it would have been workable. I thought that maybe a marraige certificate would have a father's name on, even if he's not on the birth entry, but for that I would need to search through lots of names and even assume that he got married..... there are 58 names in Northampton and Hardingstone, and that excludes one or two instances of twins.
If I can find contact details, maybe I'll ask Annie's daughter again and see if there is anyone else who might know a name.