OP, I put my DC through private school after returning to the UK. It was a good school. However, honestly I don't think it was worth it. My DC did well, but I think that was down to DH and I, not the school. A lot of my DC's peers did not do well in their GCSE's and A'levels. A private school does not mean that your DC will do well. It is just a school with a bit of a nicer atmosphere and smaller class sizes.
My youngest didn't want to stay at their 6th form for many reasons, so he moved to our local great state school. My goodness, as soon as he did he went off like a rocket in his academics and he made lots of lovely friends. The teachers were much better. They are more professional and actually care about the kids. I can't believe the attitude of some of the teachers at our private school.
With hindsight on my side, I wish I'd sent them to the local state schools with tutoring 1-1. My DC did really well, better than their peers, but that is because I have never fully trusted a school to take responsibility for my DC, that is on me and DH. I sent my DC to Kumon (not UK) then had my DC tutored in maths in the UK from year 5 through to GCSE and A'level. Both came out with GCSE grade 9 and A'level A*. I also had my eldest have some Chemistry tutoring and both my DC had 10 weeks of language boost before GCSE. The private school couldn't actually get them to their full potential despite the £££££ it cost.
Honestly, save your money. Get them a tutor 1-1 in your house or online from a good company. It will do way more than a private school.
You will still get issues at a private school. Different ones, but still issues. I found the parents extremely snobby and entitled with people thinking they could jump sets, get on sports teams and get the best parts in plays because they were 'well to do' and you know what, the heads appeased them because they often had 3 kids and threatened to take them out.
Honestly, my kids are A* students but it was the tutoring that did it, not the private school.