So, market forces and political currents over many decades seem to have fixed the amount that the taxpayer is willing to pay per year per child in state education as around £7k per year (£7,100 to be precise according to this article)
And in a well-run school with willing and able pupils, that amount of money is enough to provide a fairly decent quality of education. Obviously with more money a school could do more, but that would cost more tax, and this seems to be the level of balance between tax and education quality that we corporately as a population will accept.
In the UK the distribution of individual income means that about 20% of individual earners have more than twice the median disposable income. It's not at all surprising that some more well-off families wish to purchase a different education than that which is provided by taxpayers. About 7% of children are educated privately. In a free society the freedom to choose to educate ones children outside the state system is important and I don't think anyone is saying that it should be illegal to spend ones spare income on education if one chooses, only that this shouldn't be subsidised by the tax payer.
The above linked article says that Labour will abolish the tax advantages of private schools and use the money to fund state schools. We've had thousands of threads which go over and over how the practicalities of achieving that would be complicated (it would require a rebuilding of charity law from the ground up. Let's not get into that again though) but setting that aside, you are only talking about creaming an extra 20% of what is spent on 7% of pupils - although the rocketing of school fees might drop that to only 6% as a lot of self-funders can only just afford the fees as it is - and then you spread that among the 94% of pupils in state education. I've done the maths and that works out as less than £100 extra per pupil per year in state education - that's not going to make much difference.
To actually level up state education to the kind of quality that would begin to make private education obsolete because so many fewer feel the need to opt out of it, would take an injection of income into schools of more like £3,000 per year per pupil. That would be what was needed to get class sizes and facilities to a level that is more similar to the private sector. That would require about £30 billion pounds more per year into the education budget - there are about 30 million tax payers in the UK so that would require each tax payer to pay about £1000 per year more tax. Or if you made it progressive, that would be an extra £625 per tax payer for basic rate, £1,875 per year (3 times as much as basic rate payers) for those who pay at the higher rate and £5,625 per year (9 times as much as basic rate payers) for those who pay at the highest rate. This would raise the required £30 billion per year.
For comparison, the changes to National Insurance coming in next year to fund social care are expected to raise £12 billion - barely a third of that. So the kind of tax rise required is phenomenal.
Do we as a population want to see the kinds of tax rises that would be needed to actually level up our childrens education? Could a political party ever be voted in on a policy of tax rises of that magnitude in exchange for creating a state education sector that is good enough to make private schools obsolete?