Here’s a thread from last year from an extremely talented British applicant who had considerable success: http://talk.collegeconfidential.com/international-students/2056643-finding-an-intellectual-college-for-a-clueless-17-year-old.html
But the biggest difference I perceive is that you want to apply for sciences (although fortunately not Eng/CS). It’s going to be much harder to stand out in that competition when top US domestic applicants (and probably even foreigners) are far more concentrated in high paying, career oriented quantitative subjects. Very different to the UK where the competition at Cambridge will be similarly fierce for English and engineering or computer science and classics. That makes an undergrad degree in the UK followed by a masters in the US a potentially better path to consider.
Also, the US system is probably more interesting to an arts student from the UK due to the breadth of offerings, conversely many U.K. science students might dislike the required general ed courses and essays.
In contrast to the thread I linked above, where she spent time visiting to pick schools that seemed to be a fit, you seem to have a fairly generic list of top schools and big city schools. That doesn’t do much to convince the reader that you’ll be able to explain why you “fit” with each school in a US admission process that is incredibly “holistic” (ie cares more about fit, including your socio economic status and sports, than your academic stats).