I think that Reading is one of those universities which are underrated. This forum, and other media, may fuel obsessions with rankings and perceptions of prestige, but if you look beyond those things you may see that places like Reading are good universities. One of my colleagues in chambers holds a Chair in Law at Reading, and she is a good scholar and teacher.
I add that the reason why barristers at leading chambers tend to be graduates of a small group of universities is not that chambers recruit on "prestige", but that graduates from those universities tend to perform well in selection processes and pupillage. Graduates of other universities are not excluded from consideration. Many chambers (and law firms) now recruit "university-blind". All depends on the attributes of the individual candidate.