The bigger picture here is that I have a DNA match with a woman living in greater Liverpool. We believe her grandfather was my uncle James. He married a Sarah Stokes but had mental problems already when they married, and was eventually put away. I was hoping this birth cert would list Sarah, not Alice, as the mother. Given the oddity of omitting the name of the hospital, though, I'm wondering how accurate the rest of the cert is!
I will look for adoption records and other birth records next. The RootsChat community is great. Thanks for your help!