Do be aware when comparing rents in halls to private lets that halls include all bills including internet. Student lets (usually) don't. Private rented is usually still a bit cheaper, but when you factor in bills, the gap isn't always as big as it first appears.
Birmingham- Wide range of options to suit different budgets both with halls and I think in terms of student lets in the city. I imagine there will be lots of opportunities for part time work in the city.
Warwick- Halls to suit different budgets. Will have to live off campus in second year. A lot of students chose Leamington Spa, which isn't cheap, and they'll have the costs of getting to uni each day too. Coventry is a cheaper option for second year, but less fashionable. As it's a campus uni, finding part time work may be trickier.
Cardiff- Doesn't appear to have a really cheap option for halls, but some are more affordable than others. As I understand it, rents/CoL in the city are going up, so second/third year may be more expensive.
Southampton- I don't really have any experience of Southampton, sorry!
Nottingham- Again, I don't really have much experience.
Bristol- halls are reasonably priced (given the cost of rent in the city). Private rented in years 2/3 will be pricey. CoL in the city, even as a student is quite high IMO. BUT lots of part time jobs available in the city.
Bath- Again, they don't appear to have a really cheap option for halls (unless you are willing to share a room). Again, in second/third year CoL/rent will be quite high.
Loughborough- Again, I don't have that much experience of loughborough.
Hope this helps a bit!