Well things have moved on since I last looked at this family. Trish, you are right to advise looking at the marriage, on Ancestry I have found her (spelt Sarah Mirian) marrying John Nightingale in Enfield. She is said to be a minor, which still fits with all the censuses, but her father is given as William Prior, a labourer.
The William I have on my tree is down in all the censuses (with wife Susan) as a carpenter, so it looks like I was wrong with her mother's name as well.
Shame the marriage doesn't give the mother's name, which would be helpful.
Now all I have to do is find her real baptism.
Trish, your last post has come in while I was typing. I did spot that census this morning, it looks right, but I will have to double check all this.