You should probably look at the Times and Guardian league tables online for your subject of interest and see which universities have the optimal combination of quality and admissions standards. Then, email the admissions tutors at some of these places to see how they evaluate American applicants.

In general, it should be easier, not harder, for an American to be admitted to a British university than it is for a British student of similar qualifications. American students pay international fees, so the British universities are eager to get as many as they can without really sacrificing standards.