Based on how much you can spend on tuition fees and assuming a part-time LLM (throughout two teaching years) isnt an option (which would allow you to take on some part-time paid job), I think youll have to cross LSE, UCL, KCL and QM off your list even the home/EU fee is more than 5,000 pounds a year for those universities. I havent really looked into it, but maybe Birbeck College might be an option and maybe you could wait a little longer and save some more money so that you can afford a more expensive (and, in some cases, better) university?

Generally, the best and most reputable LLM programmes in the UK are Cambridge and Oxford (BCL/MJur). Other law schools might have better teaching in certain specialised fields, but none of them comes close to Oxbridge as far as reputation is concerned (which is probably one of the main factors for the LL.M.).
The odd thing is: Cambridge undoubtedly has the highest entry standards for people from a civil law background (who can only do the MJur at Oxford, which is apparently considerably easy to get into than the BCL), but it still has comparatively low tuition fees. University and College fees add up to a total amount of 8000 EUR, which is less than the London Colleges LLM-programmes (not to mention the lower costs of living outside of London, which I think you ought to include in your calculation!).
You might want to consider applying for scholarships and try to get into Cantab. if you want a fantastic, but still comparatively cheap programme. In any case, send at least 3-4 applications to universities you are considering in order to maintain all options.

Cantab=Cantabrigia=Cambridge
Fees in Cambridge are approximately 8000-8500 EUR, depending on your College Fee. I'll be paying 4520 pounds course fees and approx. 2250 pounds College fees this year.
The academic requirements are quite harsh. I don't know whether work experience really is a big factor at Cambridge. As far as grades are concerned, I got the impression that they usually take the top 5-10% of a class.
The MJur at Oxford is easier to get into, but also much more expensive.

I graduated at 15% of my class and had great work experience that didnt help me at all with my applications to Cambridge and Oxford and Ive heard from several other people that what matters the most to Cambridge and Oxford are your grades top 5% to 10% at the most... but even so, I think you should apply because you never know what might turn up...

And UK universities give scholarships and you also have the Chevening Awards by the British Council quite hard to get, but if you do get it, its a real walk in the park cause they pay for almost everything

Try the University of Nottingham and the University of Bristol.

They are amongst the top law schools in the country with very reasonable fees and very good programmes.

If you search outside London itll be easier to find cheaper LLM programmes maybe you could try Scotland as well: Aberdeen, Edinburgh, Glasgow or Dundee. The home/EU fee is considerably cheaper there cant be sure, but probably less than £4,000

At UoE, the fee is 5100 quid (for home/eu).

http://www.ed.ac.uk/polopoly_fs/1.41857!fileManager/TRPGfees%2010-11%20V11.pdf

Or as an alternative to LLM, you could, perhaps, consider a GDL/CPE from LSBU in London (though Univ. not at all well reputed) which I have been told at approx. £3280 is one of the cheapest GDL/CPE programmes being offered by any University in the UK.