We have poor schools with few resources and inadequate teachers. You get good teachers by paying more. You get good schools by investing money in them so that they have equipment and facilities.
Nah. It's more to do with pupil/teacher ratio, and not having to deal with the grinding effects of poverty as part of their job.
Public school teachers are no better than state school teachers and often much worse. They have tiny classes and don't have students who arrive at school in the morning with their stress buckets brimming over because their parents are working 3 jobs, they haven't had a proper meal for days, their clothes don't get washed because they don't have a washing machine, and one of their parents is dead. Oh, and there probably isn't much chance of daddy buying them a pony.
This is what you are isolating yourself from in your little Surrey cul-de-sac. Stop fùcking kidding yourself.
As for giving your daughters "the best start in life", have you ever considered that they would be better served by you not filling them with your pathetic neuroses that you externalise here, blaming all and sundry for your own personal shortcomings rather than pretending that social exclusion is the answer?