There are people like me instructing under Part 61, and registered with the TSA. Get an N-reg airplane, and that and the above is essentially all that is needed as far as the FAA are concerned. Getting TSA approval was a relative piece of piss and just involved a bit of faffing around online and doing security awareness training.
That's about as good as you will get, and you will have no end of hassle getting approval from the department of transport and CAA with regard to payment for training, what registration the aircraft has to be, and whether or not the instructor needs an EASA CPL.
I don't see why someone with the money (obviously) and a bit of get-up-and-go doesn't try to start up a FAA flight school in the UK. It would be a good laugh, and if you toed the line with the CAA and EASA I couldn't see a problem, only that you'd still be paying for AVGAS at UK rates, so it wouldn't suddenly be wonderfully cheaper to fly. The only bonuses would be not having to deal with EASA/CAA for licensing, 100 as opposed to 50 hour checks, no payment for certificates to be issued etc. But who would you get through the door? Not any of these tw@'s wanting to fly a shiny jet who want to go to an EASA sausage factory. There's not really any point having an FAA ticket in Europe now (or that's what they want us to believe, and are allegedly trying to stop) so I don't see a huge demand... Unless they bring in a simple, pragmatic conversion to EASA, it wouldn't be worthwhile.
As a side note, does anyone know if there are any N-reg private aircraft based at any of the USAAFE bases? Do they have a similar setup to our RAF flying clubs?
Anyway, if any interested parties want to bankroll me for starting up an FAA flight school, let's go for it.