I wouldn't rely on IO540's "the CAA couldn't give a damn approach" myself.
Article 267 in the ANO is what you have to comply with.
It says...
Public transport and aerial work – exceptions – cost sharing
267(1) Subject to paragraph (4), a flight is a private flight if:
(a) the only valuable consideration given or promised for the flight or the purpose of the flight is of a sort described in paragraph (2); and
(b) the criteria in paragraph (3) are satisfied.
(2) Valuable consideration is of a sort described in this paragraph if it is one or more of the following:
(a) valuable consideration specified in article 262(1);
(b) in the case of an aircraft owned in accordance with article 269(2), valuable consideration which falls within article 269(3); or
(c) a contribution to the direct costs of the flight otherwise payable by the pilot in command.
(3) The criteria in this paragraph are satisfied if:
(a) no more than four persons (including the pilot) are carried;
(b) the proportion which the contribution referred to in paragraph (2)(c) bears to the direct costs is not more than the proportion which the number of persons carried on the flight (excluding the pilot) bears to the number of persons carried (including the pilot);
(c) no information has been published or advertised before the commencement of the flight other than, in the case of an aircraft operated by a flying club, advertising wholly within the premises of such a flying club in which case all the persons carried on such a flight who are aged 18 years or over must be members of that flying club; and
(d) no person acting as a pilot is employed as a pilot by, or is a party to a contract for the provision of services as a pilot with, the operator of the aircraft which is being flown.
(4) If valuable consideration specified in article 262(1) is given or promised the flight is a public transport flight for the purposes of Part 3 and Part 4 (other than articles 37(2) and 39(2)).