In reply to Andrew 321:
Hill access from Newcastle is a bit of an arse, however the climbing and hills up there are great (also a very good local scene with a solid university club and a very friendly local mountaineering club, the NMC with whom lifts can easily be scrounged).
Sheffield has easy access to the crags/ hills, plenty of people perpetually keen to get out.
Lancaster
UHI - it's in Fort William
Bangor University - close to the hills, shouldn't have any issues with partners
Leeds - bit like Sheffield from what I've been told.
I would suggest looking a list of the best universities which you can realistically get a place on the course at and then strike out all of the universities which are a long drive from the crags, Loughborough, Nottingham, Leeds, Sheffield, Bristol, Birmingham, Manchester etc all have active university mountaineering clubs who you will be able to share lifts with.