My applications were well over a decade ago now but for what it is worth, I did an LLM at Birmingham. I chose it because at they had a wide range of elective options some of which are quite unusual, which I gather is the case for the undergrad as well. It also has a dedicated law library, rather than a section of the main library, which is good because frankly law students need the library and you're more likely to find a quiet desk. Birmingham also has the advantage of lots of opportunities for legal work experience in the city with annexes of law firms and local chambers, and courts with some really interesting cases, as well as good transport links to London (helpful for interviews, or, if applying for the Bar, banking some Inns dining sessions early). They also have excellent sports facilities which was important to me.
I did not however apply there at all for undergrad for two reasons which you may want to explore if they are still the case if matter to you: One was that at the time they didn't have an international year abroad option. The other was that at the time they didn't guarantee you accommodation if you didn't put them as your first choice on UCAS (and my top two were always going to be Oxford if got in then Bristol or Warwick).
In a professional capacity I have worked with groups of students from Southampton and Exeter unis. Whilst they are comparable academically, the vibes are very different.
Bristol is IMO worth a look. It has many of the same advantages as Birmingham but is a less intimidating/safer city. The course used to have some interesting year abroad options as well - check if still the case.
Nottingham has for a long time had a strong reputation for law, and again the course used to have some interesting year abroad options - check if still the case. However, I was really put off when I went on an open day, and didn't apply: I would say its one to visit.