The last I heard from the CAA was that they were not going to 'facilitate' any more out-of-EU JAR training - but they can't 'ban' it.
So, potential US trainers could probably apply for approval, but there's nothing to say that the UK CAA is obliged to process the application quickly, or cheaply. And the cost of the inspection will, no doubt, include costs involved by the assessor.....?? Club Class return from Gatwick to wherever, plus accommodation and subsistence on top of an hourly rate, perhaps?
The practices regarding safeguarding and marking of JAR PPL exam ppaers in some, though hopefully not all US schools is also known to the UK CAA.
Train in EU for a JAA licence
Train in the US for a FAA licence
Train in Oz for an Australian licence.
....and convert from one to another in an agreed manner.