UK uni’s have websites web sites list this information. The Times lists rankings. Full pay to the UK is only cheaper than tippy top full pay in the US. Being a cashed up American would influence only in the way that it would help you in the USA. Competitive UK schools are competitive globally (LOL at 3 APs, good luck with that at the tippy top), but like the US, there are much less competitive schools that would be delighted to take full pay students.