The question is this. How do you log JAA P1 time in their aircraft? If you ask them that question then let us know? We need to know will you be the sole person in that aircraft at all times or will you be required to take either a safety pilot or instructor with you? If the latter two then I would be very sceptical about it all.
Some poor sod posted a few weeks back about how he went for a ride with an instructor pal having paid the school at P1 rate and had his hours not accepted by the CAA. The instructor was of course logging it all as P1 as even though to all intent and purposes he was enjoying 50 hours worth of jolly with a guy that had a PPL. Moral of the story has to be - fly by yourself or at least someone without a licence/instructor rating.