I know what it's like, I was researching on behalf of someone else too. I thought I'd found the person we were looking for - like you, I found that there were no other records in the same name - and it turned out that this person had been adopted but was nothing to do with the family of my friend... rather embarrassing really! I came to the conclusion that the best thing to do is to go through the proper channels, which I haven't any experience of as my friend has decided not to take it any further at the moment. This website might help:
http://www.ukbirth-adoptionregister.com/resources.phpI would have thought that as your friend is looking for her deceased mother's records, she would be allowed to persue an enquiry as if she was the one adopted - I don't know for certain, but I would think this could be her next step.
Christine