"There might be a reason why the government is lax to change charity law to put more onus on public schools to prove that their area of benefit is not for the self-interest of the privileged few who use them. Just saying..... "

Hmmmmmmmm!
Better review status of the following outfits then:
             Institute for Public Policy Research (IPPR)
             Charitable status
             Known as training ground for many of Labour’s special       advisers
             Demos
             Charitable status
             Smith Institute
             Education and research charity