I've never heard of a actual definition of a private flight, a commercial flight is defined. A private flight is one that isn't commercial and to put it in the old terms; the purpose is not for reward by the operator. The operator is not defined from ownership. It has been long established that training flights are not commercial. Consider this, if this document had any truth in it then henceforth no club member hiring a club aeroplane could venture abroad without prior permission from the CAA. The CAA has never had the authority to demand advance notice of a non-scheduled flight into the UK. A flight plan is required for international flights of course but they are not routinely forwarded to the CAA and do not require permission for VFR.
The home Office/Border Force have the power to prevent the entry if it has good reason but that wouldn't include defining the category of the flight. The Dept. of Transport/CAA do that but have no immigration or customs powers. The CAA cannot prevent a flight unless they believe the aircraft is unworthy, the pilot is not qualified or is unfit and the flight is believed to being operated illegally. They must not obstruct the free movement of flight operating properly in accordance with ICAO.
Have you seen this document and are certain that it is genuine. Are you possibly holding the wrong end of the stick? Parts of what you have quoted is very similar to the Border force requirements; that allow a flight to operate internationally from a non customs designated airfield and this has nothing to do with the CAA..
Last edited by Fl1ingfrog; 12th Nov 2021 at 22:19.