Unfortunately, even if you were to come here and study at a UK university, it's very difficult to stay here once you finish your studies. I'm sure someone else has more information on exactly why this is, but I've known a lot of American students in Edinburgh, and a few years ago several of them were able to stay and work after graduation, but recently, due to some immigration changes, none of them have been able to stay and work. All but two have had to move back to the US. One is now engaged to a UK citizen, and the other was fortunate enough to be asked to be a lecturer, but I know the latter is a very rare case.
That's because the Post-Study Work Visa (which is discontinuing this April) is only valid for two years. After that, you must find another way to stay in the country, and that's often difficult. Getting engaged or married is one way to do so, and getting sponsored by a company or organization is another (the university lecturer is a good example of this).
I looked into moving abroad after college for a long time. Getting my Master's is how I have accomplished that. The other options I looked into mainly involved working in the US for a few years at the least, saving money and getting a fairly good wage, then applying for a work permit, but I don't know if that's an option anymore with the recent changes, and it's not a very quick solution.
My MA was expensive, but I got complete support from US Federal Student Loans, which I'm now slowly starting to pay back (ugh!). However, I don't know if I'll be able to stay long-term if I want to. Years spent on a Post-Study Work Visa (which I'm waiting for now) do not count towards your years working toward citizenship or any other residency status, if I'm correct. Plus, as I mentioned, the PSW Visa will not be an option after April 5th, 2012, so would not be available to you unless they bring it back while you're over here (not very likely in my view, although I think it's a mistake).
My friend was working in the US at an international marketing firm for about a year, and just now got transferred to their London office since she is fluent in Mandarin and can work with Chinese clients here. I'm pretty sure this is a case of her company sponsoring her, and they can justify doing so since fluent Mandarin is probably something a bit more difficult to find in marketing professionals.
My last advice: If you're into government stuff, look into the Foreign Service. The FS staffs American embassies across the world. I thought about doing it, but I don't really think you get a choice where to live and I was set on England because of a boyfriend. My friend's grandparents met in the foreign service and travelled the world together. They say it was always an adventure. Here's the website:
http://careers.state.gov/officerGood luck with everything!
