It really is the independent school parents who are being asked to subsidise state schools and not the other way round.
They are paying taxes towards state schools (fine, generally no one arguing with this) while not using them (again fine, same as anyone who doesn’t have kids). But they are now being asked to pay a whole lot extra ostensibly to pay for the state education of other people’s children,* when even the most insanely wealthy state parents aren’t being asked to contribute any extra.
If that’s not a subsidy I don’t know what is!
*of course, the money isn’t ring-fenced so isn’t actually going to go towards state education at all but let’s not let facts get in the way of things.
FWIW: my children go to our local state school.