I'm a private school parent in a well-off part of the country. But I also went to a state school in one of the poorest areas of the country, and did so at a time when state schools had been run into the ground by three successive Tory governments (plus ca change...). My memories of state school are of:
Grinding poverty among a large part of the student cohort.
Crumbling buildings and infrastructure.
Class sizes of 35.
Teachers struggling with crowd control
No differentiation, ever.
Frequent teacher absences and a string of substitute teachers giving us word searches day after day to keep us occupied
Special needs left entirely unmet.
Assaults - physical and sexual, and not a teacher in sight to do anything about them. Not that they wouldn't have cared, just that there weren't enough of them.
Despite this, I initially sent my child to a state school, with no intention of going private, and only removed them from state to stop the slow-motion car-crash that was unfolding. I was obliged to do so by the 1996 education act, i.e. ensure my child receive "efficient full-time education suitable to his age, ability and aptitude, and to any special educational needs he may have".
re: "what private school parents think state schools are like" I would say in a nutshell : crumbling, overstretched, under-resourced, and as a result failing many children, despite the best efforts of many excellent and committed staff.