Will a masters strengthen my training contract/vacation scheme application?

A better question to ask is - why are you wanting to do a masters?

Is it because you think it will help you stand out academically?

In which case, I wouldn’t proceed. There’s a reason why most law firms ask for GCSEs, IBs, A Levels, and undergraduate university module marks and degree classifications. That’s because virtually all training contract candidates have them (or equivalent). It means they can easily compare your results against others to determine the strength of your academic record. Doing a masters, for instance, to try to remedy a poor undergrad degree is unlikely to work and is a waste of your time and money. You’ll also notice no firm requires a masters as part of their academic criteria.

But what about if it’s at Oxbridge?

Despite the advice above, there are a few firms that are known to like a candidate who has studied at Oxford or Cambridge. There could be some merit of doing a masters (such as the BCL at Oxford) to impress such firms but on balance, I still think focussing your time and resources on other areas of your application (such as work experience) could prove more rewarding.

I have a genuine interest in the area

If you’re genuinely interested in the area of study, that’s different. In which case, you should do the masters. Just be ready to explain it at interview, particularly if it is non-law related!