I have 4 children - the oldest two went to an academically selective independent London day school, third child is extremely bright and goes to a SS grammar school (no tuition, also gained scholarships but wanted grammar school). Fourth child about to start local state school.
Over the years I have come to realise that success is much more down to individual drive than anything else. I think parents like to feel that a private education is a passport to every success in life but that simply isn't true.
When I look back at the many cohorts of children I've known, there have a wide variety of outcomes, personal and academic, and it doesn't appear to depend upon the price tag attached to the education. I would say that private education is no guarantee of academic success every time and the most academically successful child I know personally was state educated (but bright, very determined and suddenly became very driven at A' Level).
We can comfortably afford school fees but, bar one school that DS did not gain a place at, didn't feel that the other independent schools we were considering fitted our requirements or really warranted the £20K of tax paid income that was demanded. That sum of money can be used to support and educate in numerous ways.
So we shall see. I have no doubt that my youngest child will achieve similarly to his older siblings (RG degrees, Masters etc.). It's just that it will come without a hefty price tag. That money can be used to benefit him in other ways.
One other thing I have noticed is that a private education does not necessarily ease their path to university or once in the workplace in the way it once did. In fact, I would go so far as to say it can be a hindrance. Elite universities are under pressure to seek a more diverse cohort and in the world of work (except possibly law and politics) it really doesn't count for much. We always used to say that we were paying for them to have a nice time and I think that much was true.
Boarding schools, I have no knowledge of. I asked youngest child if he would like to go to boarding school but he was horrified so I left it at that. If he had been interested, I would have considered it as I think for the right child it can be a wonderful experience.