You can probably get a 1 br place for $600/m rent plus bills. GBP is weak atm. So ballpark you could probably do it. There are probably even cheaper cities or towns in UK too.

COL is high in London and cities around it, but way cheaper in other parts.

FWIW I'd recommend other places over Nottingham, though. Birmingham is a vibrant "second city", with low prices and good connections to London. Several decent universities. Manchester is cheaper still. Southampton is cheaper than London and has good culture and a good university. Glasgow is a cheap and rapidly rejuvenating city.

Nottingham is IMO pretty dull. Maybe the parent commenter has better experiences though.