Are there international applicants with work experience completely outside the UK who have made it through the US firms’ processes?
Speaking from personal experience and my surroundings (LLB and most work experience done in multiple EU countries, LLM in London) , it seems that American firms actually like more “obscure” profiles.
I have mostly progressed with global/US firms rather than magic circle/silver circle etc. A friend of mine (same spiel as myself) ended up getting into A&O through Shearman Steling before the merger 2 years ago, and another friend made it with Debevoise.
What I imagine is that American firms establish themselves in London to expand to Europe more broadly , so having more “European” profiles doesn’t hurt.
Not sure what your profile is and where you have your work experience, but regarding European profiles I think there’s an angle that can be sold. If you’re from anywhere else, I think the most important is to try and leverage whatever you have with the firms that connect well with whatever work experience you have ie geographical reach of the firm and languages etc.