Hmmm. I also think it depends on the school and what you expect to get for your money. I have signed DD up for my local private school, after much soul-searching, as I just don't think the local state schools will give her the tools she needs to have the opportunities I hope she will have.
For context, we are in an area which has too few primary schools for the number of children - a situation that is only going to get worse. The (previously outstanding) school we live in the catchment for is now only rated 3 by ofsted and comments in the report include that girls are not encouraged to do mathematics/science. Despite not having factors which could explain low attainment in the nationwide tests (e.g. high numbers of students who do not speak english as a first language, high SEN student numbers who struggle with academic, etc), the school has inadequate resutls in maths and english. Add to that the fact that the school apparently has a billion rules telling parents what they can and can't do (e.g. the contents of packed lunch boxes), and I am very unhappy about the thought of sending my child there. If we even got a place - DD could instead be shunted off to one of the nearby village schools, which would be OK if we had any way to get there that wouldn't take over an hour (no trains, buses only once an hour, and we don't own a car).
And that's just the primary level. Secondary schooling around here is worse - but not so bad as to give students special consideration by university admissions. Instead, it is just mediocre. The highest results for a student last year from all three of our local secondaries were 6 As and a couple of Bs. My DH does Russell Group university admissions and he took one look as said that unless there were many red flags for the student (e.g. disabled from a single parent family on benefits and the first to go to univeersity in their family), that student wouldn't even get a look in at his university.
In contrast, the local private school has excellent facilities (sports fields, a climbing wall, a swimming pool, amazing IT centres), goes up to V1th form, gets brilliant results (including taking GCSE maths a year early - in which the whole class usually gets an A*). There is also a contract with the school in which the school sets out its obligations as well as outs - nothing like the state school 'contracts' I have heard about which are remarkably short on detail of what the school will be doing and which I would be returning unsigned with a note asking exactly what they considered their obligations to be. I want DD to enjoy school, get decent results (not looking for a genius - just want her to do well enough to have options), and I think that the private school is the way to do it.