You seem to be in dire need of an education in economics and finance.
Parents who send their kids to private school pay income and property taxes.
In the vast majority of cases, they pay far more in tax than the people who send their kids to state school.
That extra tax acts as a subsidy for the folks who send their kids to State schools as there is no tax rebate for this in the UK.
If you want to improve the funding for State schools, you will have to adopt a more progressive local property tax like they have in the US.
But then again, that also means people sending the kids to state schools would have to pay higher property taxes as well.
Funny how that works right?
The reason why state schools are failing is because of funding. And the reason funding has been cut is because we have an aging and sicker population (more tax revenue being funelled to the retired for pensions, healthcare and social care), as well as a very narrow tax base (upper 10% of income distribution pay 60% of the taxes, with the bottom 30% paying much less because of the £12.57k tax free anount).
Scandinavian countries have superior schools because everybody pays tax. Same with property taxes.
So if you want better State schools, that means the bottom 50% will have to pay up as well.