Having just done an LLM, it's not necessarily going to improve your ability to be a better lawyer. I'll use myself as an example:
I have a LLM in Diplomacy and International Law with distinction. Now, this is useful if I want to work in organisations where legal knowledge and the skills you learn are an asset, but not necessarily a general training contract. There is a law firm, Voltera Fietta, who only take candidates on their internship schemes if they have a postgrad (and possibly PhD). This is because they're firm is incredibly specialist.
So what I'm trying to say is, it depends. If you did an LLM in a specific area of corporate law that may aid you with understanding how things work, but it doesn't mean you'll be better as a lawyer in ten years as someone who didn't. It does, however, show a prolonged passion and drive in a particular area which some firms admire.
What I will also say is, just because you did law doesn't mean you have to be a lawyer! Law degrees are spectacular foundations for the skills and abilities (and yes knowledge) necessary in multiple areas of work. Civil Service, political parties, NGOs (especially!), policy roles, etc. Don't feel you're trapped to follow the TC route. I've been in academia now for five years (finally escaping!) and I know it's shoved down your throat to go for a TC. There's a lot more out there. Make sure that what you do is something that you actually want to do rather than being what you 'think' you should do!