Is there any major problem in applying to PhD program in US after getting BSc and MS in UK? I'm considering getting my BSc and MS in UK instead in US, since I prefer specialization rather than diversity in education. However, I'm not sure whether or not this choice will affect my chance to attend a competitive PhD program at an American university, since people who get MS tend to stay in UK to get PhD. This route may have the following problems:


I will have to take some extra courses in my grad school in US to make up for classes not taken.
I may be disadvantaged in admission because of differences in the educational systems in the US and the UK.


Considering these problems, should I rather stay in US to get BSc and MS? Or are they negligible? For me, it's the best if the time spent to get BSc and MS will be as short as possible. This may seem strange to people in US, but I want to consider the merits of education in both nations, so I can find the course of education which is the most suitable for me. 

(I want to study molecular biology.)
Let me clear up an important distinction between graduate school in the US and the UK:


In Europe, the master's degree is generally a pre-requisite for admission to a PhD program.
In the US, the master's degree is not required for admission to a PhD program, and you normally apply to the PhD program with only a bachelor's degree. You can obtain a master's degree as part of the PhD program, but this is by no means a universal requirement. It varies between universities and even departments within a university.
In the UK, options are somewhat ambiguous. You can apply for a master's and PhD program at the same time, while others may require the PhD in advance.


Therefore, if you are admitted to an American PhD program, you will take courses in graduate school, because that is the equivalent of the master's phase in the UK.

Other than that, there's no inherent advantage of applying or attending bachelor's or master's programs in the US or the UK.