LPC with a master qualification

Not really - a separate LLM from a well known Law department is more valuable than essentially a tack on piece of paper. You're better off just finishing the LPC then applying for TCs, and possibly some LLM programmes as a backup. That said an LLM isn't really worth much when you're actually working in a TC or as a solicitor proper unless you're in a really arcane and specialist area of law (like taxation or something maybe) - or even a huge amount during the application process. It's more of a Barrister thing afaik, where it's very common and well known programmes (like the Oxford BCL - which is in essence an LLM, if not in name) can make a notable difference.

My understanding is, for Solicitors, they barely care about LLMs from even decent universities unless it's like, Harvard LLM/Oxford BCL level - a random qualification such as this is even less likely to matter to them. Unless you went to a non-target UG and then got an LLM from a target school and are applying for magic circle firms or something similar, it's very unlikely to be important, and quite likely to be a waste of money (this is for LLMs - extrapolate then the lesser value of this top-up).