I have no idea what you do with your spare time, and I blame you for nothing. This discussion isn't about you.
Selective schooling divides the population at about age eleven, and adds another and arguably even more significant element to the social division which private schools foster. When a university says "80% of our students went to state schools", it may omit to mention that most of that 80% went to selective schools in affluent areas.
I can't see that abolishing fee-paying schools would increase state funding for education. Removing the charitable status of private schools (which is not justified in many cases but is justified in some), and making them subject to VAT would raise some funds, although not a vast amount in context. I think that Labour should go ahead with that policy, which has been talked of for decades, but doing so won't wave a magic wand.
I would prefer that all schools should be free at the point of use and non-selective, but I doubt that will happen any time soon.