Unless you have so much money you don't care about the cost, I don't think the question is really "is it worthwhile to send my children to private school" but "is it worthwhile to send my children to private school compared to the alternative?"
Lots of posters on here saying their state alternative didn't meet their child's needs, for example, so private was worth it for them. Their neighbour's child probably had different needs, and private school might not have been worth it.
The other comparison of "alternative" is what you would be doing with the money if you weren't spending it on private education. In our case, we looked long and hard at private schools and decided it was better for me to work part time when the children were younger so I could be about after school (I would have had to work full time if we'd gone private) and they could benefit from that; and to put money aside for house deposits (we couldn't have simultaneously paid private school fees and done that).
And our local school is in the category of what I would call "good enough" - it's not amazing (GCSE results just below average) but we supplemented with tutoring, extracurricular activities and parental involvement. Would the DC have had a nicer all round experience if they'd gone to private school? Possibly, if we just looked at the actual "being in school day to day" bit, but as a long term broader picture including benefits as young adults, state school looked better.
(I went to a private school, was bullied and left with my mental health on the floor. These problems are not absent from private schools).