Playing, I think it is possible. Difficult, but possible.
I think a handover period of ten years or so, during which time state-funding of church schools is gradually reduced, and the saving put towards state education, would be doable.
In many cases, I imagine that the Church would hand over control of a school to the state, which could probably be effected in one move, over the summer holidays. Teachers, heads remain in place, but whom they report to shifts from diocese to state.
Extra money would be needed to buy the school from the church, but that would be a one-off capital expend.
Others become entirely voluntary-aided. Or private (a whole 'nother thread)
As far as political will is concerned, I agree, it's a problem. But not one that is impossible to overcome.
Presented as a snatching away of middle-class 'rights', it's a series of shrieking Daily Mail headlines.
Presented as a response to the increasing religious division in Britain... will still be Daily Mail headlines, but far less shrieky.