I'm not sure I'm buying this entirely as stated, OP. Private schools are not all academically selective, far from it. For parents who cared even in the most technical about their child's education or social future, regardless of whether or not they were decent people or good parents, here would have been lots of other options between a 'prestigious' private school and a comprehensive/a sixth form on a sink estate. And surely there were other options for affluent established MC people (especially as you describe your mother as a snob) whose child needed a chance to start over at sixth form, other than a 'WC school'?
Also, to be frank, you don't write like the child of an Oxbridge-educated surgeon and charity director. You say you speak RP, but you also say that your teenage self refused a further attempt at private education with the words '"I don't want to go to NO school'. Or were you already rebelling against them by performing WC-ness? Is that what guided your choice of partner and your hobbies? I know a fair few surgeons, and I can't think of one who would list their hobbies as 'bingo, football, watching soaps' -- it seems pretty unlikely you were around those as pastimes in your childhood., surely?
It seems to me that you have decided MC-ness is a matter of bad parenting, rejection and failure, and WC-ness as warm, nurturing etc.