Given our restrained national finances, this would have two benefits. It would repeal a legislative quirk of the 19th century on the one hand that benefits private companies, and would be genuinely progressive on the other. Both the state and private sector would benefit in the long run.
Fee-paying schools would be able to demonstrate their social function in terms of cold hard cash, the state sector would benefit from a new revenue stream. If some private schools can't cut it, they would shut and their pupils would either move to better private schools or into the state sector.
We are all in this together – this would be a way for the education sector to show this.