Neither Bath nor St Andrew's offer law as an undergraduate subject. OP, you may be able to judge the quality of Academic007's advice about law degrees by the fact that he or she didn't know that.
As for the Russell Group, people often mistake correlation for causation, and overlook the fact that many law firms and barristers chambers recruit "university-blind".
The success of Russell Group graduates in legal careers is an example of a self-fulfilling prophecy. The Russell Group universities tend to have the best resources and they attract high achieving students and academics. They may (not must) deliver a qualitatively better law degree.
Take Oxford, for example. Some criticise the fact that the undergraduates only have two optional papers, but they study the core subjects intensely, and this can be distinctly evident when you're up against an Oxford law graduate barrister in court, as I often am (armed with a mere history degree and a PGDL, although nowadays I have decades of experience, so I've caught up). To cheer Academic007 up, I've been up against some redoubtable opponents with law degrees from Nottingham.
By contrast, I know someone who has what the University of Law calls a first and she doesn't know what a contract is. So quality counts, but quality isn't just a question of branding.
The reason to go to a Russell Group university is that they are good universities. There are several other universities not in the Russell Group which are good, and the notion that you can't get into a legal career without a degree from a Russell Group university is untrue. People are hired as individuals. Nobody gets hired simply on the strength of a CV that says BA (Cantab) or LLB (Nott).