Speaking as an FAA CFI based in the UK... Honestly don't bother trying to do training and (especially) testing for FAA qualifications in the UK. It will be no cheaper, the cost of the tests extortionate, and the standard of instruction questionable (as many UK based CFIs are so far out of the loop with current FAA training standards). You would be much better doing the training in the US, with a school and instructors who know the system, within their airspace.
I have done training for a few people over the years towards FAA instrument ratings in the UK, and even though it means turning work down, I'd rather people went to the US than trying to muddle through it all here. They can still visit me for differences training and Flight Reviews or IPC, but for any "proper" training towards certificates/ratings all you'll get from me are links to the FARs and the web address of US based schools!
