Whopity,
By auctioning a ticket the flight becomes Public Transport because money has changed hands for the purpose of the flight, Article 157.
Public transport and aerial work - general rules
157 (3) Subject to the provisions of this article and articles 158 to 163, an aircraft in flight shall for the purposes of this Order be deemed to fly for the purposes of public transport:
(a) if valuable consideration is given or promised for the carriage of passengers or cargo in the aircraft on that flight;
I disagree with your interpretation of the above. The beneficiary of the valuable consideration would need to be the operator of the aircraft for this to be the case. Under the charity arrangments the donation of the flight is a gift from the operator to the charity. The auctioning of the ticket is a transaction between the charity and that donor. Accordingly, there has been no valuable consideration either made or promised to the operator of the flight. In any event , you selectivley and unhelpfully quote only article 157 which defines SIX EXCEPTIONS! These are set out at Articles 158 to 163.
5.2 Exception No 2 - Charity flights (Article 159)A flight will be deemed to be a private flight for all purposes if the only payment is to a registered charity which is not the operator of the aircraft and the flight is made with the permission in writing of the Authority. (A general permission has been issued in an Aeronautical Information Circular (79/2005 (White 114)) so that pilots do not have to approach the CAA each time, provided the flight will be conducted in accordance with the operating conditions set out in the annexes to the AIC.)