I think you are thinking of the aristocracy and the very small percentage of the population that have serious family wealth. I would agree that these people generally use the top private schools. They are also a tiny proportion of those that use private schools and most private schools aren't like Eton etc.
I don't live in London or the home counties but a relatively wealthy area in the South. £200k is a very high household salary. Only 2% of households have an income of £200k so it is absolutely ridiculous to suggest that they are merely 'reasonably affluent'. I know you are trying to downplay the fact that actual wealthy people go to state schools but the fact that the tax payer is funding these people's children's breakfasts is laughable. To then have the cheek to charge VAT to others that feel forced to turn to private schools because they live outside the hugely expensive catchment for the outstanding school and only have a choice of poor choices is disgusting!
Btw just to add, I have a foot in both camps at the moment and find it bizarre that I am being charged VAT on school fees for one child whilst being offered a free breakfast club for the other. It is true insanity!