Hi [USER=3039]@studentdelaw786[/USER] there are indeed some US firms that are more oriented towards university prestige. I would assume that is likely a corollary of the so called 'campus interviews' recruitment system in the US, where firms go to the campuses of 'elite' laws schools and interview applicants there. However, I will specify that (i) not all US firms have this focus in the UK; and (ii) even the US firms that do have this focus end up having non-RG trainees - while it may be an important criteria, it is not an overriding consideration.
As for whether an LLM at an RG university would increase your chances with US firms, I think that is possible. However, I do not think the improvement in chances will be so significant to justify you doing an LLM only for this reason. An LLM is an important commitment of time, effort, and money. Moreover, in this period you could use your time to more effectively improve your chances in many other ways: submitting more high quality applications, to work experiences, networking, improving commercial awareness etc. I would only consider doing an LLM with a primary motivation to increase chances of getting a TC if you have already done your best to improve your chances in all these other ways.
Finally, although you have not asked this directly, I will say that even if your ultimate goal is to work at a US firm, you do not necessarily have to start your journey there. It is significantly easier to lateral at a US firm as an NQ than to get a TC there. Firstly, because as an NQ you are very profitable for a firm (in excess of 1 million/year at some firms), whereas as a trainee in many cases the firm is actually losing money in training you. Secondly, because the US firms commonly employ a model where they will take on substantially fewer people as trainees than they need NQs and then they will simply attract many NQs from other firms by offering higher salaries. As such, provided you are still interested in their work, I would not disregard the possibility of training at a different firm and then moving to a US one. In my vacation schemes at top US firms I have met plenty of people from a non-RG university who trained somewhere else and then could lateral without much difficulty.
