Just finished my degree at LSE....it's a small but interesting university..you can find all sorts of things to do in London. All kinds of social events and tons of reading...anyway you won't feel bored. I don't like the winter here cause it gets dark so early (at 3-4pm)... summer is much better. So hopefully you have chosen the right season to come.
I have to say I was in a pretty similar situation...as one of my recommenders said he would comment only on my intellectual ability, but not on the interpersonal aspect....The problem is I can't easily replace him with another because of some history...