How would you rank the following schools in terms of international prestige in the field of international law:
Edinburgh, UCL, Kings, LSE

LSE
UCL
King's
Edinburgh (though maybe I'd rank it above KCL in international law, as there are some good PIL professors there)

KCL
UCL
LSE
Edinburgh

KCL has a better international reputation while UCL has a excellent "local " reputation (In England , UCL is considered to have a slight advantage). In Europe and Asia it is clearly KCL. In the Americas, LSE has a better reputation although it's more of a general reputation than a Law related one.

1. UCL= LSE
3. Kings
4. Edinburgh

Good Gosh is right.

cr is right!

I think CR1 is right. KCL is much more popular in central europe and parts of Asia. Much more than UCL. LSE for Law is a clear third in my opinion.

Bear in mind how much a foreign presence is dictated by a university's commitment to attracting students from those areas.

In the UK, UCL and LSE are clearly ahead of Kings. That's not to say Kings is a bad university by any means - it's excellent and has a very strong reputation. But then the same could be said about Edinburgh.

What's important is that you can justify to law firms why you picked that institution beyond its reputation.

even in England, the choice will vary according to the specialization. for ex, you go to UCL for jurisprudence,PIL, legal theory, KLC for finance or competition law...

exactly, the OP was inquiring about international law, hence my suggested ranking...

KCL
UCL
LSE
Edinburgh

For PIL, I'd say 1) LSE, 2) King's, 3) UCL, 4) Edinburgh for the schools' international reputation/exposure. Many legal employers in North American haven't heard of UCL or Edinburgh.

For private international law, I'd say 1) King's, 2) LSE, 3) UCL, ?) Edinburgh. King's has a strong specialization and focus in private international law, while LSE thereafter has international clout over UCL. Personally, I have no idea what reputation Edinburgh has in private international law.