Hi Sharon,
My thoughts on this is that if there is some doubt over the true name of your gt gran (being Annie or Hannah) and the only definite information you have on her is her year of birth and her father's name of Solomon who habited the area of West Ham at some point, then I would say that it isn't impossible that she was in fact Fanny Lee, daughter of Solomon and Maria. Of course a birth certificate of some sort would be ideal, either for Annie or Hannah. Do you know when exactly she was born? Any idea of a month, for example? That would help if you did find a possible birth record.
The Fanny and Solomon quoted above were reportedly born in Plumstead and Greenwich respectively but certainly a lot of the Lee family settled in the East London area.
I have this Fanny Lee on my tree and the fact that I don't have any information on a husband for her, nor have I seen any elsewhere, does at least open up the possibility to us to not discard her for being married to someone else...(does that make sense....? I'm not sure if I made it clear). If there were documented proof that this woman had husband and family elsewhere, we would have to eliminate her from the list of possible ancestors for you. If she's 'spare' and 'unattached', it improves the chances.