I often hear this point about tutoring coming up on threads like this and I think it's missing the point entirely.
Abolishing private schools won't make everyone's lives equal. Wealthier children will still have access to tutors and more after school activities and nicer holidays and more help at home. Unless the PP is advocating for some version of stalinist Russia then I doubt she is suggesting abolishing all of that too. And most wealthier children will have the means and the help at home to do well at most schools anyway.
But private schools and grammar schools are a very clear and damaging cause of inequality. They are divisive in a community. Stopping someone being tutored wont benefit anyone else, but making everyone be educated together does benefit others. I'm sick of hearing the standard middle class dilemma of moving areas to access better schools, or paying to go private. The children that are left behind just have to lump it in their local schools, abandoned by all those with money.
Grammar schools are the worst in my opinion. All this pressure at age 10, and if you fail, you instantly have less of a chance of doing well. Parents desperately paying tutors from year 4 to get their kids in. Imagine a country where everyone is invested in the quality of the local schools, everyone is educated amongst a true mix of their local community, and actively learns about the lives of others. Everyone really cares about the quality of their local schools, and outcomes are actually a fair representation of ability rather than just a representation of who paid more for their education. Look at the attitudes of so many government MPs who were educated only amongst their own kind, completely clueless about what living in the real society they represent actually means!
There are areas in London where an astonishingly high amount of people go private. People basically either go private or leave the area, leaving sink schools there noone wants their precious children to attend, it totally divides a community.
The best option in my mind is a lottery system. Everyone in an area gets allocated a local school, not done by distance so there is no rugby scrum to live on the school gates, but children are educated amongst people from the whole borough, no private no grammar. There are parts of the country where this lottery system is already in place (although still a few independents around). There would be a huge drive to improve the state education system by ALL involved, not the wealthiest abandoning it, or moving round the country into little middle class bubbles leaving all the problems behind for the poor less privileged folk to live with.
I actually went to one of these schools that people run away from. I narrowly missed the catchment of the school my parents hoped for and did absolutely fine, so I'm no hypocrite and I won't be putting my kids in private or grammar schools even if there was an option.