I agree with both Turnoi and CL. The FAO should not be involved in the actual process of your teaching. His/her purpose is exactly as CL stated.

On the other hand, you may have meant your dean or administrative head or even a Chinese person who has taken on the role of coordinator. At any rate, I think it would be simple enough to just go ahead and make a lesson of it. You could even make it pretty humorous. As a North American, my students always got a good laugh from me trying to imitate a British accent. Ultimately, though, if you teach in China long enough, you'll encounter lots of situations where you are having to teach from material that goes counter to what you're used to. There are a lot of American teachers teaching from British published ESL/EFL books and the other way around. It's often amazing what they expect you to use.

I think, though, that if you're willing to show a little flexibility in this situation, things will work out fine. If I were trying to put together a lesson like that, I'd ask for a little extra time. Maybe use some power point material regarding some of the more obvious differences between common British and American accents. You can establish at any point that your accent is a regional accent from England and due to that you just can't pull of an American accent. Then show them - give them something to laugh at. Personally, I'd also make it clear in a somewhat humorous manner that Clinton doesn't actually speak with a standard accent. He's pretty ding dang Southern. But not that Texas kind of Southern like Bush, who couldn't speak his way out of a paper bag.

Another upside to being flexible in this situation is that it may pave the way for you to be more creative in your lesson planning without having to rely on material that is probably out dated if not totally irrelevant from a Chinese student's perspective. At first you may have to show that your using the text as a guideline, but eventually, as long as the students are learning what has been set out in the syllabus, you'll get more and more free reign in terms of lesson planning and classroom procedure.

I also agree with Turnoi in that this is nothing to run away from. If you're in a fairly neutral situation, my advice would be to hang out and learn from it. If it becomes totally untenable, then of course you'll have to leave; however, believe me, there's a lot worse out there.