I just finished up my MA in museum studies in Newcastle, and my experience
with finding internships is that you will be hard pressed to find a paid
internship.  We were required to do an internship as part of our degree, and a
number of my fellow classmates were turned away from museums, and they were
offering to work for free.  As an American, you would also have to either pay
to get a work visa through CIEE, or get your employer to get a work visa,
which again, is unlikely.  You might be better off getting a temporary work
visa through CIEE, working a non-museum job to pay the bills, and volunteer in
a museum.  That said, living/working/studying in Britain is a great
experience, and I highly recommend it.  Good luck!