This literally isnt true. There are almost no private schools that can actually be affordes by families on average incomes unless they have family wealth meaning no rent or mortgage, or wealthy grandparents paying.
Average uk day fees are 24k.
Median full time salary is 39k. Lets assume there are two parents both earning that - 78k.
After tax & minimum pension contribs its about 30k - £60k combined.
Average uk council tax: 2.4k
Average gas & elec: £1.6k
Average rent: £17k
Food: 7k
So already there's only 32k left & we haven't covered student loan repayments, insurances, water, phone/internet bills, tv license, transport & fuel, cleaning products, clothes & shoes,
Most people have more than one child so fees would be pushing £50k a year out of post tax pay.
There are very, very few children from average income families attending private schools.