Standards Document 39 Section 3.4 for PPL training :
certificates entitling them to conduct ab-initio instruction and authorise solo flights
Thefore if you are giving instruction at a UK FTO and do not hold an FAA CFI you are not qualified to do so.
Heads up to all instructors without the CFI - the CAA mentioned this the other day to our FTO which deals with US Based training.
Also I know a certain FTO which just had an FAA FSDO visit regarding this - which through fear of their over reaching "legal theats" cannot be named. How does the student gain the right to fly solo in US airspace? They can only do this through a student pilot certificate which to fly solo must be endoresed by an FAA CFI. So part 61 does apply because there is no other way - said school was using non FAA CFIs - which meant those students training for a UK JAR PPL could not legally fly solo in US airspace. Cue visit from FAA FSDO, resulting in instructors who were not qualified for the FAA system, and are not qualified for UK CAA either due to the requirements for FTOs training abroad.