There seems to be a suggestion here that you (a Brit) can do your FAA instuctors rating etc in the US then work off some of the cost there. That is NOT going to happen! The FTO might let you but uncle Sam will not unless you marry someone while you're there!
The advice 'train in the UK to teach in the UK', is good advice...Take it!
Even when desperate, UK FTO's will go for a UK trained instructor over a US trained one, EVERY TIME!
If you do your FI course in the US you will have to 'unlearn' a lot to instruct well here. It is very different over there....not bad, but different.