I lived in Birkbeck last year, honestly I know nobody wants to get put there but it's really not as bad as it seems! The PEOPLE you are living with is way more important than WHERE you are living. If you move into birkbeck and get on with your flatmates, I would HIGHLY recommend NOT trying to move, because you could get put with people you don't get on with!
Obviously it's up to you, but I just thought I'd share my opinion.
Let me know if you have any specific questions!