Well I'm not from the USA, but have to get current very quickly in order to be ready on day 1 at the job, therefore will it be legally acceptable for me to undertake a simulator session in the UK that covers the syllabus?
Well, I'm sure this problem has come up before. You need to find out what exactly your new employer considers as "current", then get your UK provider to give some sim sessions to train and check to whatever standard your employer wants. It's not so much what the FAR's say as much as what your employer / foreign government wants. It would seem that "legal" is what they say is legal. If it's an FAA certified program in an FAA certified sim., then I'd guess you'd have gone a long way toward meeting anybody's requirement - but I can't say for sure.
I'm working in India, and a some sims in the US have programs that are tailored to DGCA requirements for a FATA - pass the program with the requisite prior experience and you're considered current by the DGCA (usually
). Possibly there's something like this for your situation. In any case good luck!