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.

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.