hmm, that's a term set to get the emotions running isn't ....how are they "subsidised" by the tax payer --?
Do you think private schools get state grants out of taxes for their facilities or something?
What you really mean is why don't they have to pay taxes like any profit-making companies with shareholders except they are not - institutions whose primary purpose is educational - and that is usually associated with a charitable purpose.
Or do you want fees to be hiked by forcing private parents to pay VAT on top of fees ?
thirdly, have you thought about how every home-grown child in private is actually saving tax payer money by not taking up a place state tax payer funded place ?
So if you tax the private schools, private fees will be even higher making them even less accessible to the middle classes and only accessible to the very wealthy or global elite - how will the system cope with even more middle classes seeking and competing with existing state pupils for even more selective grammar (when there are far fewer places around) and leafy comp places at the additional cost to the tax payer (especially when some of those fees will just go into private tutoring which people already complain about in terms of ordinary (working class children competing for state selectives))?
Tell how that would actually benefit anyone at all, state or private?
Taxing foreign non-EU students to study here in privates might make sense because their parents have not already paid into the system as tax payers and because they may not stay here.
You could also just as well morally argue that you should get a tax break for sending your kids private as you are paying taxes for a free state education and you have children who could qualify and are entitled to that.
It all depends on what side of the fence you sit on.
Why not do what France does and actually subsidize private places thereby taking burden off the state ?
We need new thinking to solve the issues of alternatives that are no god enough instead of lobbing of the same old emotive grenades (private vs state; selective vs. non-selective, catchment vs open selection) on the pretence that somehow that will achieve "levelling" but are actually only about taking away decent choices, even if not all can benefit.