Article 259(2) does not define a club or a club environment;
I think they mean 259(3):
(3) Aerial work consists of instruction or testing in a club environment if it consists of the
giving of instruction in flying or the conducting of flying tests for the purposes of this
Order in an aircraft owned by, operated by or operated under arrangements entered
into by a flying club of which the person giving the instruction or conducting the test
and the person receiving the instruction or undergoing the test are both members.
But it still doesn't offer any guidance as to what a "club" is.
If you look at the privileges of a Flight Instructor ANO Sched 7 you will see that all instruction has to be given in a club of which both parties are members.
I can't find any such restriction. Where are you looking?