Are you interested in academic jobs? If so, what I was told in my former field (Classics) is that British PhDs are not as valued in the US because they do not involve as much preparatory coursework but go into research sooner. Then again my adviser was an Oxford PhD and he got tenure, so that perception is not insuperable.
Your aiming high is a good thing. If academia is the aim again, it’s better to not go to grad school than to go to a non top 10 in your field.
I don’t know as much about industry unfortunately. But like I said, grad school admissions are relatively straightforward. Grades, test scores, prof recommendations, research, that’s about it.