"Did you apply to any other Master of Laws program?"

Specifically, I want to know how a university might view a "Yes" answer.

Thanks in advance!

First of all, you have to answer the question truthfully.

My understanding is that if you apply to several law schools it demonstrates a genuine desire to acquire an LLM and to study law, whereas if you don't apply to other schools you might not appear to be as passionate about the subject, since you're banking on a single chance instead of trying hard to get in anywhere you can. On the other hand, not applying to other universities might demonstrate an extreme preference for the school of application, which might be considered an asset in your favour.

I hardly think these ideas have any primacy over grades/experience/letters of recommendation etc though, and I urge you to just tell the truth whatever it may be.

As far as I understand it, most schools use this sort of question for statistical, rather than decisional, purposes. They want to know what other schools people are applying to so they have a better idea how to target potential students in the future. It's possible it may be used at the margins for decisional purposes, but I would doubt it in any sort of negative way. The only circumstance where I could think of it hurting you is if your personal statement says how much you want to do X or want to study in Y, but none of the other schools you are applying to fit that profile. Like, if you said in your personal statement to KCL how you've always wanted to study in London, but the only other schools you've applied to are in the US.

I second NYC_Charles's post... I don't really think recruiters would look down on you if you named other schools, unless they haven't got any resemblance to what you've stated on your application.