It's a policy of envy so a massive protest of disruption does fit. I have no skin in the game as we have moved to an area to get into an outstanding faith or ex grammer school (our choice likely to get either). My mortgage now reflects the area but we are only likely to stay for 3yrs before moving somewhere cheaper to get a bigger house having renovated this one.
The kids coming out of the private system are likely to be at transition points in the majority of cases so parents can simply move to get the school they want.
Having saved on school fees a tutor is also easily affordable so you aren't stopping privilege in fact all you are doing is driving it underground making it harder for universities etc to give contextual offers.
The kids also already have contacts through their parents and are likely friends with the lawyers kids etc outside of school. It's the kids of successful working class parents without those connections who will miss out the opportunities to build connections.
If he really wants more money for education what would be an idea is a system something like go fund me that parents and local people can contribute to with gift aid for individual schools. Our PTA raises thousands per year for fun things if the schools need it for essentials I would rather it went direct to them.
If he actually set out a spending plan something like defense, education and health with a focus on reducing the deficit instead of vanity policies like this he would be more relatable to everyone not those who envy others!!