independent regulatory bodies

That's interesting.

Surely a real regulatory body should be a country's Ministry of Education where inspectors have powers authorised by law.

Independent bodies raise their funds for inspections from their association's membership fees, so someone of an illuminati nature may very well think that relying on membership fees means they can't really be totally independent, especially as NABSS says on http://www.nabss.org/index.php/en/about-us

"The National Association of British Schools in Spain (NABSS) exists to defend members' interests...."
Defend member's interests against whom?

And what sanctions would these Training Centre Clubs be able to dole out to recalcitrate members - maybe take away their membership cards?