You guys are conflating “school name” with the actual educational experience a student gets at different schools.
MIT used to publish a very handy and illuminating chart showing GPA and LSAT scores (nothing else) of its law school applicants and where they got admitted. It was very apparent that MIT grads benefited from the “MIT has grade deflation” reputation. Even accounting for “splitters” (law school-ese for people who have a huge disparity between grades and LSAT scores), MIT grads at every GPA level were doing better in law school admissions than the law schools overall stats would suggest. And in some cases- MUCH better.
But this has nothing to do with the “name” and everything to do with the actual education, pedagogy, and rigor of what students at MIT are actually doing for four years. And I’ll hazard a guess that this works at most undergrad institutions where graduating with a perfect GPA is rare, and also have an extensive core (so the law school hopefuls can’t “protect” their GPA by avoiding classes they’ll know they’ll struggle in.)
CC likes to claim that all colleges are the same, a kid can go anywhere from everywhere, etc. And yes, a kid CAN go anywhere from everywhere, but all colleges are NOT the same and pretending that they are is unfair to the students who post here looking for advice. Law school adcoms are looking at actual transcripts in addition to looking at GPA and LSAT scores. Phoning it in as an undergrad may (or may not) get you in to law school with the right LSAT score, but getting OUT of law school if you haven’t learned to write, think, analyze, and work your %^& off will be a challenge.
OP- why not go to college in the US and spend a semester in the UK? That will scratch the itch without complicating your law school aspirations.