as a black person as well, i know manchester the city is very diverse, but i cannot tell you about the student population and last i checked there's a direct train from manny to cardiff. same with bristol and london (imperial). i would say bristol and imperial both have a reputation (from what ive heard) for being very posh, but imperial seems more diverse (mainly bc its in london) than bristol. i have a black friend in leeds and she says its very diverse, however im dont think there's a direct train from cardiff but its probably just one change and same with york, but i dont know how diverse york is. you should also take into account that york is a campus uni, so even if york itself isnt very diverse, the campus might be moreso and it will also be easier to be around other students. the others are like semi-campus/city universities (not too sure on leeds), which i would say makes bristol the least appealing choice at the moment even though its closest. i would say your best bet is manchester, leeds or imperial, however london can be very overwhelming and expensive, but definitely check out their campuses either in person or online.