Difficulty being admitted to good PhD programs in the UK
You seem to be operating on the assumption that "I have my own funding, therefore, I can go wherever I want". That is simply not true. Taking on a graduate student is not only a matter of money, it is also a significant investment of time on the part of the advisor and believe me, at top departments, time is a more scarce and precious resource than money. If the professor does not see a reasonably good chance that this investment is going to result in a comparably good outcome (i.e., a student with high-profile publications and a strong thesis), then very likely they won't take you, even if you bring your own funding.