It's certainly not a place associated with 'poshness' (i.e. it's not a standard post private school destination such as Exeter or Bristol), but as a leading university it does attract those with stronger academic results, and, predominantly, the vast majority of people I know are 'middle class'. As far as I could tell in my accommodation last year (the supposedly 'posh' one), everyone just got on wherever they were from, it really didn't matter. I don't think the proportion of 'posh' is high enough here for it to become an identity thing.