My situation is probably a bit different than yours but I have my degree from Oxford & I returned to the US about 3 yrs ago...I believe most European degrees are highly regarded & I had no problem having my marks translated to the US equivalents. However, most consideration is given to your lsat score...as such, really prepare for it. You should register with lsac.org as soon as possible--you will find nearly all of the information you need on their site. I was able to take my lsat here in the States but I think you should be able to register to take the exam at an administering site in the UK. If you have an exceptional score, you will qualify for various scholarships--depending on the school, you could possibly even get full tuition paid. Alternatively, you should be able to take out a personal loan depending on your credit in the UK--I know that Barclays was prepared to provide me with a loan to pay for my tuition if it came to that. Student VISAs are not that difficult to obtain, particularly if you are highly desired (lsat score/degree marks). Hopefully, I've answered most of your questions but please feel free to email me. Best of luck!
P.S. Are you planning to practise in the States or the UK? I know of several people that have US law degrees & work at a London firm...just curious.