In 2017/2018, five years after graduating, graduates in Law from Bristol were earning £10,200 more per year on average than those at Nottingham, where graduates earned £2900 more per year on average than those from Manchester.
Source: legalcheek.com
It just so happens in these particular universities' cases that this corresponds to average entry grades and average research quality too. Source: The Complete University Guide.
It also happens to correspond to the order of percentage of students who went to private school.
However, for Law, both edurank and topuniversities.com regard Manchester as better than Bristol as better than Nottingham.
Nottingham has sometimes been more successful than Bristol with numbers of students going in to Law firms- Nottingham might have a larger department. In more recent years, Bristol has tended to pull ahead of Nottingham, which has tended to pull ahead of Manchester.
Manchester University has been teaching Law since 1872.
Bristol's Law Faculty was founded in 1933, although law teaching was happening there in the 1920s.
Weirdly, for quite an old university (1881, roots from 1798, current site from 1928. Awarding degrees from the University of London until 1943 when it received a royal charter, officially becoming its own awarding body of the University of Nottingham in 1948), I couldn't find out how long Nottingham University has been teaching Law.
I should point out that, nowadays, it is not necessarily the universities names that is affecting people's prospects or salaries but the general aptitude, confidence, and connections of the student, and the fact that wages in professions down South are generally higher than up North, with housing generally costing more down South. However, each student is an individual, not an average.