University of Bath. All the way.
I was in the same spot as you not 4 months ago. I get social anxiety sometimes, although it's very mild. Before going to uni, I was extremely worried about going into university especially because of how some aspects of uni life seem to be potrayed in the media, and on TV and whatnot. Suffice to say, I am pretty insecure at times, and I thought I wouldn't be able to participate in anything come uni time, and that everyone would be nothing but short of being overtly extroverted.
That wasn't the case in bath. I've met people from all walks of life, and personalities I thought I would never come accross in university. It has been incredible so far. The atmosphere, and the people in it, has so far been nothing but stellarly supportive and friendly.
If I could recommend anyone a university for any reason whatsoever, it has to be University of Bath. It's no surprise really after I found out it has won the no.1 student's satisfaction award in the UK for 2 years running :P