can we please have an honest discussion about this? i honestly don't blame LSE for rejecting you and those like you. I mean you're fresh out of school, you've never had a proper day's job, you don't read legal material, you've never gone to your local courts, you've never done barrister shadowing, you don't know how to draft legal documents and your only source of passion for law is the tv show Suits? how fantastic can your UCAS statement be? needless to say, the outcome is obvious?
as for cambridge it has nothing to do with your age. most Oxbridge students apply 1 year/a window cycle before they actually start uni proper. as a result of this sly manoeuvre, outstanding students like you who apply in the year that you want to start uni will often have to face extremely stiff competition from other equally spectacular students.
you're still young so if you need to take a gap year then do it. if it means you get into a better uni according to your beliefs, then do it. but don't get into the sick vicious cycle of applying more than 3 times in 3 consecutive years just so you can get into a better uni. i know many people who have done that. in some cases, it payed off. in other cases, some of those friends of mine simply did not have the desire to purse law anymore and simply did another course altogether.
if you think that the top unis are very good in terms of teaching quality then you're gravely mistaken. i did a post on this so click on my profile to view my previous posts and you will discover a wealth of information.
and this really bears repeating. i really don't see any significant difference between your remaining 3 choices. I'll go for QMUL if i were you. Only cos QMUL sounds nice than say Bristol or Durham
do update us here on how things pan out for you.
nottingham has always been very slow.
which unis did you apply to and have you gotten any offers? did you do A levels or the IB? what were your grades and what was your LNAT score?