I came within a hair of going to the University of Edinburgh several years ago for a research PhD. I strongly encourage the OP to take kilted scholar's commentary to heart.

The program I was considering at UofE was nothing at all like similar PhD programs in the States.

A taught masters level degree is probably attainable for someone with a high quality American undergraduate degree, but with a very steep learning curve attached. If you are going to be sucessful in a UK research PhD you should, 12-18 months into your masters, have essentially the same grasp on your PhD research project that an American student has with less than two years remaining before oral defense of same.

UK research PhDs are not for the faint of heart, and a taught Master's on the ground might be the best possible preparation for an American student hoping to pursue one.