I empathise with your conundrum OP!
I've been there... In the end we moved AND put the DC in independent schools however our youngest is at state school as it just seemed a better fit. The ones at independent school have cost us so much money it's hammered us. Independent schools are good in many ways but we ended up having to move them both again for reasons out of our control - one Indy school closed down!!
I think you need a joint income of at least 180K pa in my experience and it seems affordable when they are in reception etc but in a flash they are wanting ski trips, LAMDA, music lessons on top, plus lots of other trips. Uniform and PE kit costs are laughable - about double for basically the same stuff 🙄.
Having experience of a few different schools along with friends who are also in similar situation, we all agree DONT BE FOOLED by the advertising and marketing of private schools... the advertising and reality are usually worlds apart!!
Ask yourself what are the main reasons you think it's better?
For 2 of my DC is was simply their mild SEN and basically came down to the smaller class sizes. Which you don't get in state schools.
I'd also say that the out of school clubs can be more diverse, however, mine only really go to 1 or 2! These can easily be accommodated out of school for much less!
The sports equipment is good at private school although absolutely no better than at my youngest DC state comprehensive where there are 3G pitches and lots of sport fields etc.
A spanner in the works has been that my DH was made redundant a couple of times too which caused so much worry and made things very tight!
One thing I will say, tongue in cheek, is that the staff are often a lot more polite and friendly at private schools, after all, they are a business and want your money! If you leave, that mask slips as we have found....!
If I had my time again I would think really carefully about what it is you think a private school can offer your child and you?
They all vary, some are elitist hot houses and others are small and more nurturing.
We moved from zone 5 in London to a market town in the suburbs- different vibe and it ticked many of our school boxes just by moving there tbh.
Sorry this is a little disjointed, I keep getting interrupted!
Good luck with your decision.