For post graduate (professional exams only like SQE/ LPC/ law conversion year) 80% of UK students and future trainee solicitors us University of Law or BPP, therefore it will come up again again but ONLY for those professional exams as big law firms use those institutions for the post grad exams through which they put their future trainee solicitors. However for undergraduate just about no one who does well uses any of those institutions.
For those wanting to qualify as solicitors in the UK if you have a different degree already even things like in History then you would want to do s law conversion PGDL and SQE courses instead of an LLB and ideally would find a law firm to sponsor you and pay for those courses. So do work out your aims first rather than thinking an LLB is the right choice if you have a different degree already. In addition a few people will not need even the PGDL/law conversion because of how they plan to qualify and will just need SQE an their 2 years working in a law firm etc / training contract.