@secondaryquandries It's a totally valid concern, particularly with VATs on fees coming as well as generally inflation and the pending recession.
I don't think there is a right or wrong answer as it will depend on your child and what your alternatives are, including working less to be available to support the kids more with activities and schooling.
For us, our girls are academically high ability and so we think benefit from and enjoy the pace and depth of an academically selective school offers and we aren't near any grammar schools. One of my daughters is also very musical (perfect pitch, can play music by ear since very little) and sporty and really gets the most out of private school's richer co-curricular offering.
With that said, though, if we couldn't afford it, it would be the first thing I'd give-up. We live near outstanding state schools and so it's very much a luxury rather than a necessity in my mind.