Hello annie,
I had a similar Liverpool problem with a lack of registered births. I believed that I had found "my" family, but how to tie them in, as it were? How to prove that they were in fact siblings?
Well, all I could come up with was buying the marriage certificates of those that I believed to be siblings, and hope that the father's name and occupation were the same as for my direct ancestor. I already had the marriage certificate of my own direct ancestor, so I bought a couple more of the supposed siblings. Well, it worked - albeit it was a bit of an expensive way of doing it.
But then, it was my direct line, so it was definitely worth it. Otherwise, I would still be wondering.
It proved that they were "a family".
Of course, it did not verify the mother's maiden name.
But that may yet be possible, if I find even one of the birth certificates of the siblings.
Good luck with your search,
UKgirl
P.S. What I should have pointed out was that the occupation at the time of marriage was quite different from that on the Censuses. For that reason I could not be sure that it was the same family, until confirming that the other siblings showed the same father with the same change of career. Then it was sure that they were members of the same family.