There is no 'best' Uni for Law - you dont come out of any Uni with a barcode of your forehead that instantly guarantees you a great career or lifeling happiiness. And no, LSE or 'London' does not give you any astonishing advantage over anyone who went to any other Uni with a string reputation for Law.
Yes, there are Unis that ask for A* grades, but remember that doesnt mean that you will like the course or enjoy being at that Uni anymore than any other. As with all UCAS applications, the advice is to have 5 choices with a range of grade requirements so that you spread the risk of 'no offer' and you have lower grade offers to use an Insurance choice.
And btw, LSE has a student population that is 67% overseas students, the majority of them Chinese.
There is nothing wrong with this of course, but it may impact in your 'student exoerience'.