Thanks for the information. As I understand, there is not a chance for me to get into the PhD program to the top 20 universities even with great GRE, great GPA from a top UK university and 1 very strong LOR. But to be honest, I don't get how people normally get into this program after their undergraduate degree. For example, I am pretty sure there is not any undergraduate program in the UK which help you to build your research experience; it is just about taking modules and their coursework. Is it different in the US and students can build their research experience in the undergraduate or the universities except everyone to gain that from outside of the university for 1-2 years and apply to the PhD after that?
I heard that universities in the US do not like the gap between the studies, and this is the reason I want to apply this year in the first place. Also, research-based MS sounds great for building that research experience, but as you said, there is not any fund for that which prevents me from doing that but thanks for your suggestions.