I don't have access to the article, but a friend who does tells me that it reports that just 3,000 children will drop out of private education this year as a result of this measure.
If that's true, it means that about 600,000 will continue to pay average fees of £15,000 per year, for a total of £9 billion. 20% VAT on top of that is £1.8 billion. That's £600,000 per child that drops out. It won't fix the national debt, but it seems like a nice little earner for the Treasury.
Also, if more parents do take their children out, they will probably spend the money saved on consumer goods and services - the new cars, holidays, etc, that parents of children in private education often report sacrificing - which will also attract VAT.
So whatever the social/moral/ethical/jealousy/loony-lefty aspects, claims from some quarters that this "won't raise any money" are probably misplaced.