I completed my A-levels from an extremely competitive public school and ended up doing law at King's. I originally got an offer from the LSE but decided to go for Oxford again. During the process, I got rejected from Oxford and the LSE. To be absolutely honest, I would have definitely gone to the LSE if I could turn back time.
I got an offer from UCL but felt it was too 'mainstream' for me and I think I made the right decision. While students studying A-levels are obsessed with league tables - which I completely understand - I would really recommend they research the actual course structure offered. For example, in the 1st year of UCL law you study 8 subjects whilst at KCL you study 4. I actually prefer the KCL structure, since you acquire a very deep understanding of the fundamental subjects (contract, criminal, european, public). My close friend at UCL often asks me for help in contract. This depth leaves you with professionalism and the extremely valuable opportunity to consider the law properly.
Indeed, I would go so far as to say traditional employers prefer the intellectual rigour of the KCL course.
You should also consider that the Centre of European Law,Centre of Medical Law and Ethics, British Institute of Human Rights (BIHR), Centre for Crime and Justice Studies (CCJS), Centre of British Constitutional Law and History, Civil Liberties Research Unit (CLRU) and the Tax Research Unit are at KCL. European law is one of the most overarching and important issues in law at the moment - and the KCL European lecturers and tutors are amongst the best in the UK and Europe.
I feel that KCL is let down by some of the subjects, but as far as the Law School goes I would strongly recommend it. Especially so if you are considering international law.
There is also a University of London - Columbia University Double Degree program, which most people don't seem to know about. This is a four year course, where you end up with a LLB and JD. This would usually take 6 years to complete separately. Indeed competition is fierce, but it will make you exceptionally qualified for international law.
For those unfamiliar with the US unis, Columbia University Law School is amongst the top 4 in America, and arguable the best place for international law in America.
Anyway, I hope everyone gets into the uni they want and approach the entry process as a useful experience in itself. Employers don't just look at what uni you're from (although, of course it could give you a head start). Remember to get involved in additional activities that set you apart!! Thousands of excellently qualified law students graduate every year from university fighting for a place in the City!!