Hey nimaland,
I was put in the same position as you earlier last year, because I was studying in Australia and had received an offer from the University of Melbourne to read Law (with Arts), as well as offers from universities in the UK. And I'm going to LSE in October...
The University of Melbourne, Sydney and (I think) ANU have incredibly reputable Law faculties -- however, Melbourne U is the only Australian university which is ranked highly globally (18th in the world). In contrast though, universities like LSE, UCL, Cambridge and Oxford are all renowned, and to graduate with a Law degree from any of these institutions gives you a PHWOAR factor world-wide -- more so than Melbourne U can offer.
However, with regards to other UK universities such as Kings, Warwick and Nottingham... I'd put them on par with Melbourne U, and Sydney and ANU. (I don't think UNSW is particularly renowned for Law, but I could be wrong since I wasn't looking to apply interstate anyway).
These conclusions have been the result of about six months of research, and I have a friend who is currently studying Commerce/Law at Melbourne U and she's extremely jealous that I have a place to read Law at LSE, so I guess you can see this debate from two angles.
However, I urge you to consider the questions chalks has set down as well, because they concern the long-term impact of your decision.
Good luck with everything, and keep us updated!