I hold a first degree in Law and a postgraduate diploma in English private,I wish to findout if its possible to take a LLM degree programme through distance learning

The key is in what subject do you want to take an LLM by distance learning?
These are the LLMs offered via distance at Edinburgh:
LLM Innovation, Technology & the Law
LLM Medical Law and Ethics
LLM Intellectual Property Law
LLM Information Technology Law

You can review the programmes by following this link. http://www.law.ed.ac.uk/ahrc/teaching/

We offer online LLM degree concentrations in:

(1) Anti-Money Laundering & Compliance
(2) Wealth Management
(3) Trusts and Estate Planning
(4) E-commerce
(5) International Tax
(6) United States Tax
(7) Finance
(8) Bankruptcy

check us out at http://www.llmprogram.org or http://www.tjsl.edu/llm_programs