There are loads of amazing ones - and some not so amazing ones. But for some you need to live on the doorstep in very expensive postcodes, or get aptitude places, or spend the relevant number of years praying etc.
There are lots of reasons people also choose private - SEN, poor choice of local state, tradition, wanting to have smaller classes and less disruption, worry their children are easily led and likely to coast, wanting very selective and no grammars etc.
But, when you have potentially been spending £££ for years, and now there's an extra 20%, a lot of parents with children with really high grade predictions are thinking that actually if they target a really high ask state 6th form there won't be the disruptive elements, and they can save the fee money to pay university upfront or house deposit etc. If child is already on track for stellar GCSEs, is the value added enough to keep them in private? The sports facilities, theatre and exciting extra curriculars that were so appealing when child was 11 may not be so important if they have two left feet and would rather spend their time coding than on stage.
Having recently done the calculations, a 3 year degree in London with the full maintenance is heading for £70k borrowing... and may well increase. That's a huge chunk of debt to be starting life with.