I’m surprised to hear you say that you live in London, yet none if the state schools are “convenient”, by which I think you are talking about distance? In my part of zone 3 there are three primary schools within 5 mins walk of our house (2 non-denominational, one C of E) and a further four within 10 minutes (one Catholic). You don’t say how old your child is, but have you very carefully checked the council website and made absolutely sure that you know which schools are likely to be offered to you?
The reason I’m confused is that, for us, the downside of private school was the distance (15 mins by car) so it’s odd that you are in the reverse situation and I’m wondering if some wires are crossed somehow.
Going back to your child’s age, you need to get all the information together about application deadlines for private schools as you may be able to rule some out by already being too late to apply. If applying for Sept 2023 normally you’d have done all your tours and applications by now. Some have waiting lists years in advance, though that’s not quite so common now. They will then likely have an interview process.
One advantage of sending a child to a private school from reception is if it is a “straight through school” - usually the kids in the pre- prep (years R to 2) get entry to junior and senior without having to do a further entrance exam, and are joined further up the school by kids who come from state at age 7 and 11 after intensive prep for entrance exams. So unless your child has serious academic performance issues they will not have any of the stress that bright kids applying at an older age will have. It’s all done and dusted with a gentle play-based interview at age 4.
That is a game changer. If the private pre-prep school is standalone and doesn’t have an attached junior/senior school then your child will still have to do entrance exams for the next level independent schools. The private pre prep will of course prepare them but they are still on the treadmill.
I have no experience of state primary in London. Our son’s school has great facilities, a nurturing atmosphere, food and trips included, lots of sport and 20 per class. He’s bright, especially at maths, and he is challenged appropriately. I think it is well worth it. He’s only 6 so I suppose he might still turn into a twat but he hasn’t yet, and the older kids I have met are by and large not twats either. Nor are their parents, at least not statistically more twattish than the general population. I am state educated myself, though I do work with a lot of twats so maybe I have become quite twat-tolerant, who knows..