If the checkout-pilot is not an instructor only one person on board can log the flight.
Is a check out some form of test? Surely it must be or there would be no point to it? Who is in charge? presumably the check pilot? Is he exercising a piloting function? Is the person being checked exercising a pilot function? presumably he must be or there would be no check conducted. Now what the Law says is quite clear:
79 (1) Every member of the flight crew of an aircraft registered in the United Kingdom and
every person who engages in flying for the purpose of qualifying for the grant or
renewal of a licence under this Order must keep a personal flying log book in which
the following information must be recorded:
(2) Detailed information about each flight during which the holder of the log book acted
either as a member of the flight crew of an aircraft or...
(3) The information recorded in accordance with paragraph (2) must include:
(c) the capacity in which the holder acted in flight;
and
(e) information about any test or examination undertaken by the holder of the log
book whilst in flight.
So it would seem to me that there is a legal requirement for both parties to log such a flight.
There is no reason for the check pilot to be an instructor as the flight does not meet the requirements of Art 80 but it does meet the requirements of Art 79.
People are often confused by the minimum crew requirement for certification purposes; there is no maximum requirement, that is the prerogative of the "operator". The CAA may not count certain hours for various purposes, but if there is a legal reason to justify the original comment please tell us where it is.