I'm not sure it's even just an exodus from private schools I'm afraid.
It's exactly the same families being hit: over and over again. It's looking like £4-5k for school VAT (only 1 DC for us), £4k in council tax, £1-2k in NI on pensions, and whatever other batshittery they introduce in CGT on main home/pension relief reductions/lowering the higher rate threshold (£1k extra tax if it comes down £5k) etc.
That's looking like at least £10-£12k more tax - probably more. Out of already taxed income, as pp said, so about £20k of pre-tax income gone, which we would otherwise put into pensions, during these critical last 10-15 years of our careers where we're trying to build that up.
And the way they're mismanaging the economy, there will be even more tax rises next year. And I'm starting to see that the country will be so destitute by the time I retire that they'll means-test the pension: there are already rumblings. What I think will happen is that the locks will be lost one by one, until it isn't even increasing in line with inflation - at which point at 4% inflation it would be worth 1/3 of the current value (ie just £4k) after 30 years. They'll increase means-tested benefits to compensate - but only for pensioners on low income.
So I'm starting to think that we can't afford to stay in the UK until DD finishes her education. We need to use this last 10-15 years of working to build up pensions... and we can't do that with the government stealing all our income.
International British private schools (teach A levels in English) aren't any more expensive than UK ones once you add VAT, and at this level of overall taxation even international university fees (if she does want to come back to the UK) doesn't tip the balance. But hopefully she'd stay and go to University where we settle - lower fees, a better future for her, and then we'd all be in same country long term.