Can anyone tell me what are the best British universities for copyright law in the UK? (or IP more generally if copyright is too specific).

Thanks

Edinburgh and Queen Mary are the well-known places.

I agree with Pluto, Edinburgh has an extremely strong IP programme, a large part which would be copyright if that is the module you choose: Intellectual Property Law 1: Copyright and Related Rights. You can find a description of the course here http://www.law.ed.ac.uk/pg/taught/courseoptions.aspx

If in doubt, contact the LLM programme director, Smita Kheria. She is very approachable and could easily answer your questions.
best of luck.