Hi there Kara,
I was immediately attracted to your enquiry by your surname however, it could be a coincidence!
My mother's "maiden" name was Wilson and her first name Norah, but this would have made her your aunt not grandmother due to the dates involved.I do know that as a child she was brought up by foster parents but she would have been too young to have been mother to your father, as biological grandmother.
I know of no connections to Liverpool.
Norah Entwistle married Joseph Grundy Entwistle immediately post war, in Bolton. Their initial address in Bolton was Haines Street and that is the address on my birth certificate.
Both are now deceased but their 4 children, John, Peter,(myself) Judith and Andrew live on.
I am the 2nd oldest in the family, born in 1949 so this will give you an idea of the timescale and period I am talking about.
My dear mother was in the WAFs in the war, when she met my father.
She could not have been your grandmother as she had no other children prior to meeting my father.
I believe it to be a coincidence that her first name and maiden name have connections to your enquiry, but even you must agree that it is a bit uncanny!.
Best of luck with your search though.