There is nothing on the UK's GAR form asking to define the nature of the flight (private, commercial etc.). Nor is there any box to tick on the flight plan - only that for type of flight where the choices are Scheduled Air Transport, Non Scheduled Air Transport GA, Military or 'Other' - none of which define the nature of the flight or whether the owner is or isn't on board. Accordingly nothing you are legally obliged to submit for an international flight into the UK, i.e. (1) a GAR form and (2) a Flight Plan, asks for this information, so you don't have to provide it.