Best to do this by a rah and prestige analysis:
Exeter is the most prestigious, but is also apparently full of rahs, so not that.
Liverpool probably has the fewest rahs, but is also the least prestigious, so not that either.
Birmingham is the most ideal.
Unfortunately the two things correlate pretty heavily, and rah or not, all those universities are solidly middle-class. It makes you wonder if going to a Russell Group university is really worth the pain of not fitting in.