Here are a few pointers which I have picked up, since I was in similar shoes to you and contacted a few US sschools to see what the deal was.
Firstly, if you have a 2.1, check the equivalent US score, since a US 'B' isn't as impressive as a UK one. I scored a 2.1 (67%) and this turned out to be an 'A-' in the US with an equivalent GPA of approx 3.7, so game on there. You can refer to the British Council website for details:http://www.britishcouncil.org/usa/usa-education/usa-education-advisors/usa-education-advisors-us-institutions/usa-education-advisors-us-study-abroad/usa-education-advisors-us-study-abroad-faqs.htm
(Look at the 'How do grades compare' section)
Secondly, if you want to do an LLM in the US to improve your chances of being eligible for bar exams in more states other than California and New York (for which the LLB and LPC/BVC is sufficient without an American LLM) then I suggest you at least complete a training contract/pupillage here in the UK BEFORE applying. This will greatly improve your chances.
Harvard/Pepperdine/Ivy League are not out of reach for you with a 2.1, providing you finish the degree, but they will want you to have completed the LPC/BVC to be in with a chance. I think this may well extend to other non-ivy schools-do the LPC!!!
Finally, my girlfriend is American, so trust me when I say I've looked into all available routes for Brits to qualify in the US. BY FAR the best way is to work for an American firm with a London Office and get a transfer. Firms like White and Case, Reed Smith, Mayer Brown Rowe and Maw, Coudert Brothers, Watson Farley and Williams, and Dechert will be your best bet, as they are the big US players here in the UK.
Good luck, and hope this helps you some. (I am assuming money is no object, an LLM in the US is damn expensive for British people - US$50000).