The point is that generally the better the university, the better your chance. I have spoken to a number of city Lawyers informally, mainly at dinners or events hosted by my school and they said they do discriminate and have a general baseline of what universities are good and what are not. However as you said other factors come into play, for instance they would rather take someone with a first at Exeter over someone with at 2.1 in Durham, despite Durham being the better university. If you do not even achieve a 2.1, regardless of where you went you won't be considered. So there is that, but again there is some discrimination- even if they do not admit it openly, but other factors are of equal importance of course.
But university name is quite important, even a first from London met won't help you.