Obviously these are probably all universities that you need to get the top grades to get into - i.e. the firms that automatically exclude based on your A-levels, so it makes sense peoeple from those unis get TC’s
However your uni is only one of many things a potential employer will look at. I am from a non UK uni, one that isn’t well known outside my country, and I had a VS, 3 TC interviews (at SC firms) and have secured a TC in the area I want to work in, all without my uni disadvantaging me.
Law firms look for more than just people who get into good unis - they look for good all rounders, those with extra curriculars, good grades and part time jobs. Obviously some of those people are from Oxbridge and will have an edge, but if you tick all the right boxes you will eventually get somewhere. People choose unis for all sorts of reasons - where they live, commute etc. Choose the best uni for your circumstances, with the best options on the course for you (i.e. pro bono, years in industry, study abroad as well as rankings) and do your best there. If you enjoy it you will get a better degree and be more likely to do better.