There are 32000 schools in UK.
Of them 2400 are independent.
These educate 500,000 students. Not al of these are sons of oligarchs, industrialists or politicians.
There is one Eton.
Many independent pupils are also majorly funded by charitable trusts bursaries and scholarships for particular disciplines, arts or sports. This includes special needs placements. These are bequeathed by benefactors who wish their estates to help fund specific places at the independents.
Bearing in mind that the donating estates (large and small) will have been taxed as they were earned and then in death duties , they are effectivlely tax paid. With charitable status removed schools would have to pay VAt on incomes, then increase their fees accordingly.
A significant proportion also sacrifice massively to send their kids to school of choice. By this I mean couples working longer hours, extra jobs, grandparent funding, driving old bangers, forsaking holidays etc. SELLING their hi fis....
They are not all loaded.
Adding back the 500,000 students, many with special needs, would place a significant extra load on the already over burdened and often underfunded state sector.