DH and I were both state educated, but like you, Harrigran, we struggled financially to have our children privately educated from 11.
It made me very angry because the state primary school DC attended, which was a 'good' school, acknowledged DS's ability, he was up a year and coming top in all the assessment tests they did back in the 1970s. The school advised us not to try for too academic a school for him as he might not pass the entrance exam. They said this without any awareness of what this said about the education they had given him.
Other educational authorities admitted that, because he was a quiet, pleasant well-behaved child, he would probably under-achieve at secondary school because teachers would just pass over him for not being troublesome. Nobody considered that he had any entitlement in the state system to an education that was fit for him.
He went to a good, but not outstanding, private school which nurtured their pupils. They nurtured his passion for a subject not on the school curriculum, but made him learn the basics which he would willingly have ignored. As a result I have a happy and fulfilled son workingsuccessfully in a profession he loves, even if it is not one that brings extensive financial rewards.