It all depends on what you're after once you've finished your degree. If you want to get into a big city firm then you
may have some problems but nothing is impossible. The general consensus is that the firms look at stuff in this order...
Degree Class
Extra Curricular Activities experience etc
Your Uni.
Its just that at the top end anyway Law is an incredibly elitist profession so the uni you go to does play a part in determining if you get places or not. The other problem you may have is that a lot of firms specify the A-Level Grades they want their trainees, pupils to have. The International city firms and the top regional ones generally want AAB as a minimum. This in a way disriminates against some uni's at that stage because people with those grades will obviously go to decent uni's anyway.
But wherever you go, you can't sit on your rear and coast your way into a job.
But be warned - and I'm being frank so you don't get a wrong indication -if there's an applicant with a 1st from Brunel vs an applicant with a 1st from say UCL, LSE, Nottingham etc then the one from Brunel will probaby lose out. Firstly because of the A-Level Grades and secondly due to the uni.
If your aspirations are that you want to get to the top - as well they should be- then you need to set about ingratiating yourself with these city firms early. If you've got your foot in the door then you'll stand a much better chance.
Whatever you can do to put yourself over - i.e extra currics etc - that can give you an edge, go for it.
Sorry for the tone of this post, but unfortunately Law is buggery like that!
Best of Luck anyways though and hope this post was helpful
stay cool.
B