You can take a MPhil, PhD or DPhil in Law at any university Law School. According to the University of Cambridge web site "The LL.D (Doctor of Law) is awarded to established scholars who have given “proof of distinction by some original contribution to the advancement of the science or study of law”, almost invariably in the form of published works." It goes on to say "The level of attainment required for a higher doctorate (LLD) is very substantially higher than that required for the Ph.D. degree".