Stop the Cuts - National Demonstration

That's assuming this radical change was not accompanied by any others; what if the parents' tax arrangements were altered too so that the money they now pay in school fees was instead taken in tax and hypothecated for state education? And what capital costs would there be if the existing private schools were simply transferred to state ownership? I am sure there are many local working class kids who would suddenly flourish were Eton to become their local state school.
oh and perhaps a little levy on re-insurance would raise some funds too? ;)

Taking your points in turn:

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what if the parents' tax arrangements were altered too so that the money they now pay in school fees was instead taken in tax and hypothecated for state education?

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Some very wealthy people send their children to state schools and use the money saved to pay for holiday homes in Tuscany or whereever. If private schools were abolished, it would be impossibnle to determine who would have sent their kids to private or state schools.

[B][I] And what capital costs would there be if the existing private schools were simply transferred to state ownership?***

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An interesting idea; nationalisation without compensation. It has never been tried here or in any other democracy. Mugabe and Stalin were very much in favour. Not something that will fly in a hurry.

[B][I]I am sure there are many local working class kids who would suddenly flourish were Eton to become their local state school. ***

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You are not alone in this thought. Eton has declared its intention to be a free school in the foreseeable future open to anyone who is good enough. Eton is fortunate to have huge resources. Other independent schools are much poorer but are seeking ways to spread the intake of pupils and increase academic standards. To achieve this, significant funding would be required. There is however, always the question of uptake. There are already schemes for assisted places. Take up is limited. Many so-called "working class" families, do not want their kids to board.

[B][I]oh and perhaps a little levy on re-insurance would raise some funds too?***

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Reinsurance is specifically and necessarily excluded from Insurance Premium Tax. The reason is that if a levy were to be taken, reinsurance business would not come to London and a whole industry would be lost to the competition from Zurich, Bermuda and Munich. By keeping London as the international centre for reinsurance, considerable invisible exports occur and a huge amount of tax is collected by way of other taxes such as income tax, corporation tax and vat.