Bristol probably edges it reputation-wise, but nowadays Law firms are increasingly egalitarian, once you get to the top end of UK law schools, what is important is your law school grades, try to get a first, and your Extracurriculars at uni like law society membership etc, being proactive and a good interview for vac schemes is super important, all these things are more important than the marginal difference in prestige between the top UK unis. Going to Exeter and getting a first is far far better than a 2.1 at Bristol for example.
Would say bristol is better than nottingham but not by loads, if you prefer nottingham as a city/uni go there, but i imagine the average student at bristol is slightly better than notts.
If you want a ranking:
Bristol, Notts, Exeter, Birmingham