Hi Jenn
I know you didnt ask for an advice and I apologise if I am speaking out of turn, but it was my experience when I first moved over that in the first few weeks, maybe even months, it is one's paranoia, uncomfortable-ness or desire to "fit in" that makes them stick out, not their friendliness, their accent, their dress style, their lack of knowlegde, etc. Trust me when I say that you care about those things much more than anyone else.
Why do you think people are laughing at your for being friendly? I dont live in London, and I realize that big cities are different from the towns on the outskirts, but I would really hesitate before you jump to conclusions that all Londoners arent friendly and you have to have American friends. You said it yourself - you have to give it a chance and you have to give people a chance. I hate to say it, but if you've only been here two weeks, IME, it will get worse before it gets better. Have patience and treat every person you meet as a new person, not an unfriendly native.
Good luck to you!!