This is the way I see it, not that I am any authority on the subject.
The DofT have said that the instructor must have written permission to operate a training flight within UK airspace in a non G reg. Aircraft. They have also stated that you must be a named owner of the aircraft in question to receive that training.
I see the reasoning behind this to stop FTO’s in the UK teaching non JAR qualifications. This is why you have to be a named owner in order to receive training, and the owner limit being set at 4. From what I gather this does not stop people flying N reg. Aircraft within the UK or indeed any other country. What can they do, stop all non UK Aircraft flying in UK Airspace? I don’t think that’s going to happern.
Its all in ANO 115