bristol is better for law. however, there's not a huge difference in terms of career prospects for law between the two, or for most things, besides finance where Warwick probably has the advantage. Bristol is a much better city, and you prefer something like Bristol as you said. I'm also working class and asian but I went to a uni where it's pretty white. trust me, you will fit in and you will find your group of people. you'll come across snobs, but that's true across a lot of Russell group universities. you just have to put yourself out there as everyone does, to meet the right people. my point is that don't be put off from going to Bristol because you feel it's really white.
whichever place you choose, they're both top unis and have top law schools.