I see the Labour Party manifesto (required reading) has backed away from a proposal to ban independent schools, confiscate all their assets, and share their expertise round the system. The manifesto does say that a Social Justice Commission would "advise ministers on integrating independent schools into the state sector, with a view to creating a comprehensive education system", but this is just a sop to activists, as the party knows that any attempt to implement this would fail in the courts. [See *]
This is because of what the European Convention on Human Rights – ARTICLE 2 – Right to Education – has to say:
No person shall be denied the right to education. In the exercise of any functions which it assumes in relation to education and to teaching, the State shall respect the right of parents to ensure such education and teaching in conformity with their own religious and philosophical convictions.
It's the philosophical convictions part that's key here as this extends to people not wanting their children to be educated (however loosely) by the State. Activists might bewail and bemoan and choke on their organic lentil and coriander stew, but it was never going to happen in a country where the judiciary is independent and uncowed.
I once flummoxed John Huckle's wife by saying that if ever I had to choose between living in a country which banned independent schools, and one where all the schools were independent of the State, I'd unhesitating choose the latter. You can easily justify this on curriculum innovation grounds (difference and hence choice is much more likely in the latter case), but the justification is stronger on philosophical ones – especially the right to escape a curriculum mandated and strictly enforced by a government that a minority of people voted for.
* Their cunning plan to charge VAT on school fees is likely doomed as well, as this is forbidden across the EU. You would think that they would know that. Maybe they are planning for us to leave the EU ... . Ummh.