Is studying LLB in london really that important for a career in the long run?

Basically, I have received offers from a university in London and another university in Birmingham. (They're both good for law, while not being on oxbridge, ucl, kcl level). I'm struggling to choose between them. London is expensive af and the other option is considerably more affordable for me. If I want to attend the university in London, I'll have to take out a loan

However, everyone I've talked to irl told me it's worth it to spend the extra money if it means being in London bc it'll be more helpful for me in the long run. Especially if I'm trying to build a career in the legal field. The idea is that most prominent legal firms are in London, so I will have a better chance of networking. And in turn, better chance at a pupillage later on

So what do you guys say, should I choose London or Birmingham