Is it possible to move from the university I am at at the minute in the UK, to one in New York?

You can ask your school if they offer exchange programs with any US law schools. That's really your only option that won't throw you off course in your studies. In the US, law is a post-grad program only. So you'd need a bachelors degree first, before you could go to law school. If you were to transfer to a NY university, you couldn't study law. You'd need to study something else. Then go to law school. But if you were to get your law degree in the US, you'd be unqualified to practice law in the UK, as the two systems are different; and you wouldn't be able to be employed in the US, because you aren't legal to work in the US. So consider an exchange program, or else do your LLM in NY.

1 - no, you can't generally transfer internationally (due to the differences in education and course content) 2 - even if you could; law is a post grad course in America, so you'd need to already have a degree 3 - studying in America is hugely expensive (think £30,000+ a year), and your student loan and any financial aid won't follow you there, so you'd need to be able to afford the full cost yourself 4 - studying law in another country is pointless; the UK has different laws.

you do realize don't you that law school in new york is liable to cost around £60000 A YEAR for tuition and living expenses and there is now very little financial help for overseas students

Yes you will be a transfer