Cambridge/Oxford
LSE
UCL
Kings
Durham
Nottingham
Warwick
I would place them into those three groupings but the last three are pretty much up there with the others... It also depends on what kind of work you want to go into afterwards: at the bar; become a solicitor; academic work; or other employment.
They all have their advantages but I would say Cam/Ox are best academically. LSE/UCL/Kings all have great reputations (London law has a good reputation in the city). The other three are also all very good. I especially like Warwick and would probably put it up there in the first grouping but I'm a little ambivalent...
Anyhow, with the London ones you get the city life, which some people really love. With Ox/Cam you'll experience something completely different, and obviously the workload is large, (although it'll be big at all the others anyway). Warwick has a really nice campus. The collegiate system at Durham is nice... I kind of like Nottingham but gun crime is meant to be high there; it is good though.
If I was going to apply I would go for:
Ox/Cam
LSE
UCL
Kings
Warwick
Nottingham
Durham is a great uni but personally I preferred Nottingham when I went to see them. Look at the prospectuses and get a better idea for yourself though.
I'm studying at LSE and really enjoy it. I can't really say too much about the others. Kings has a good record for getting people to the Bar but, to be fair, you can get a top job from any of those universities. It's mainly down to personal preference.