I don't know the reason why you want to do your FAA Flight Training in the UK but it will cost you much more money than if you come to the US for 2-4 weeks and finish your training. There will be no need for VISA for such a short training.
A Multi Engine airplane in the UK is ~300 pounds/hour, in the US is ~90 pounds/hour.
Go to my website and send me a private e-mail, I can help you with that :
www.passion2fly.com
