@Yesnosorryplease and that is why I said at the beginning of my post "some do. Lots don't". Whereas you made a blanket statement about private schools having ridiculous additional costs. So I was merely making the point that not all do 
Whilst I might be ignorant of the practices of private schools in your area, so are you also ignorant of the schools in my area. That works both ways, and just goes to prove the point that I was making, that people shouldn't generalise about the extra costs of private schools, that so often get rolled out on these types of threads.
But back to VAT on fees. It's not going to be as simple as Labour saying the day after a GE "Right, now there's 20% VAT on education, but only on a very specific type of education at a very specific type of provider."
At the moment VAT applies to a product (or not) if that product is VATable. It doesn't depend on whether the item is considered a luxury version of that product, or on where it is bought. For example, a loaf of bread is not subject to VAT, whether it is a Tesco value basic white sliced loaf, or an artisanal loaf made from wheat watered with unicorn tears and bought from Harrods. It's still a loaf of bread, and so there's no VAT.
So to suddenly start taxing a product depending on who provides it, and according to the perception of it being a luxury version of that product vs a basic version, is quite a departure from current VAT rules and as such will require some careful legislation.