I've been seeing your posts and feel bad for you that you're so disappointed. Why are you so keen on King's? Looking at the league tables, Nottingham is even higher ranked (although I appreciate that''s arguably unimportant). Why not just go for Nottingham and approach the whole dilemma as one where ok, you didn't get into the university you wanted, but you're getting into one that has got just as good, if not higher, a reputation?
If you're not familiar with life in London, I can assure you that for all it's good points, it's also extremely expensive, often stressful to live in because of demands on things like property, transport, etc., and overall somewhere you're as likely to hate as love. That's my input on that part of your question if you're interested.
It seems to me you've had your heart set on Kings, got crushingly disappointed which I have a lot of sympathy on but taking a year out to then reapply to the same university where you could get rejected again seems too much of a gamble to me. If it was me looking at your application and knowing all that, I might think to myself you're more interested in the university than you are in the law, your own life and time. Know what I mean? I think you should think long and hard about why it is you want to give up so much just to go to one university when you've got just as good another, if not better, offering you a place.
Never been to Nottingham but the north generally is awesome. Bristol I know fairly well. It's a well-established 'university town'. Lot of posh kids, lot of nice-looking houses. Lot of meh. That's about it. If I had a choice, I'd head north. If I was looking outside London, I'd have included Nottingham has a choice and taken it as my firm if I'd been offered a place.