potkettleblack not sure about your reference. The table about logging time gives to options for logging PIC U/S: Case J which is only for the successful completion of a flight test with a JAA or CAA examiner; Case B co-pilot performing the duties of PIC under the supervision of the PIC. Case B might look to apply except in the notes it says this is only applicable if the aircraft has a C of A requiring it to be operated two crew.
I don't actually understand how the CAA came to their conclusion as it appears to contradict other written information. However this really is an old chestnut and liable to be debated on here ad infinitum. Personally I think P1/s should be abolished as it just causes confusion for the small amount of it that a pilot gains. This case really should be either P1 or PU/T, and the deciding factor is whether or not the instructor is named as P1 and logs the time themselves (which is most likely what happened).