hello there
I was born and raised in Britain but my family are from south Asia. I have a lot of ethnic minority friends in Newcastle and they don't seem to have had any racism related issues. I'm not too sure about Bristol but I would say that unfortunately there will always be some bad apples around wherever you go. I certainly wouldn't let this put you off as the vast majority of unis are very ethnically diverse , and there really is something for everyone. Newcastle is especially good for diversity and student satisfaction.
Hope this helps.