I am currently doing the UCL LLM with the Intellectual Property Law specialism on part-time basis. In addition to what Romiras has already said, I think it is important to note that the LLM at UCL is a 10 month degree, if you do it full-time: it is a very busy degree and you should not expect to get much time to do other things such as applications - time management in that regard is possible but important. There is no time to complete your research essay over the summer either, as would be the case for some 12 month LLM degrees. However, coming from a different legal background should not be a concern. Most students in my cohort (I share my modules with full-time, part-time and flexi students) have done their undergraduates in other countries, including Spain and China amongst others, and do still perform well. Speaking from my own experience, I do like the module variety that you can choose from and it is interesting to be able to dive a bit deeper into topics of interest.
I suggest that you should make this choice based on your own preferences, as ultimately it is you who will have to complete the degree and realistically the law firms will see merit in both of them at the end of the day. If you are looking to dip your toes into learning about professional practice and might benefit from the visa circumstances, I'd go with Kings. If you are interested in a more academic approach and like the modules UCL LLM offers (you can scroll through the catalogue any time), I'd go with that one, if you think that the stress will not be a problem for you. You do not necessarily miss out on legal experience either, as you can apply for pro-bono placements with the UCL Center for Access to Justice to get some professional experience (which is what I did).
Either way, best of luck!!
Edit: I wanted to add, that in my experience LLM's are not useless. I have gotten my first VS this year and it was the year that I started my LLM. I do not think that it is a coincidence. Even if it was not directly my application form including my postgraduate education that made an impression, I think that my LLM did show my passion in law in the interview more clearly, as obviously you learn to articulate your interest in a more meaningful way.
