I will eat my hat if this happens, seriously.
Most parents are very reluctant to move kids from schools where they are happy, so couples in this position will mostly pay for kids' fees by digging into savings and using the money they would otherwise have put into pensions and kids' housing deposits, until their kids reach the next stage of education at least; the second-income earner will then need to continue earning to make up for all the various financial holes left by this, and also to pay for tutoring and extra-curricular and other things they previously got at their wraparound private school.
I'm sympathetic to many of the arguments here from private school parents, but a lot of these threats sound awfully empty to me, based on the families I know who are currently skimping on pensions and kids' housing deposits already to pay for private schools and are nervous about this already. I would be astonished if any of them just stopped working and retired to become a SAHM. There are just too many other things that need paying for these days (and women quitting careers long-term are taking a major financial risk; we all know this)
And if it goes through, I'll stop work and send my younger two to state school. The NHS will loose a senior doctor. But the state schools around us have no quality after/before school care, no after school sports etc and I won't pay for them to sit with a childminder.
That doesn't make any sense. I mean, you could easily pay for extra curriculars, tutoring and wrap around care from a senior doctor's salary and have a shit ton of money left over.