We haven't reached the end of the school year yet OP. Few parents would take a child out of school mid-year, even if they could find a suitable state place. I'd pause your glee until September.
I'm a single mum with a ds on a scholarship at an independent. I pay half fees which is still a massive stretch for me. He is half way through his A'levels. The only reason I will not be moving ds is because I was made redundant last August and my employer had to pay me a lump sum.
Luckily I was able to find another job within a few weeks so I have enough of my redundancy payment left over to cover the fee increases and VAT.
The ironic thing is, as a redundancy payment, I received the money tax free. Then I'll pay 20% VAT on fees. If my employer hadn't reacted to the Labour election win by making a lot of us redundant, the govt would have got 40% tax on my income. So in my case, the govt has lost a fair amount of tax. 🙄