Thanks for the birth certificate of Beatrice. Interesting that she was born at 3 Blantyre St, and mother's name is now Honorine WILSON (I think probably I was mis-reading her as Honoria?) with no maiden name given, of 3 Calthorpe St.
I wonder where the WILSON name comes from - unless totally made up it sounds likely to be the father's name, though why no father named on Beatrice's certificate? My feeling is that "BELL" and "WOOL" are reasonably similar, if you're trying to mislead.
You are fortunate that Herbert is with his Aunt in 1881, very tricky to find Rebecca with her changes in names otherwise.