That's not going to happen. However, my own experience of private tuition is that some parents who could afford private education prefer to send their children to state schools and pay for private tuition in certain subjects at key times - having, of course, gamed the system so that they live in the catchment area of a perceived "good" school. That's very good news for me, of course.
To be honest, there are some private schools which really aren't worth the fees. Parents send their children to private schools for all sorts of reasons, but it's not always because they'll end up with better academic results. They have fantastic sports facilities, which suit some pupils. Sometimes parents end their children to private schools because they think their children just wouldn't cope with the hurly burly of the state system.
Having said that, there's no doubt that private schools were better resourced to cope with this pandemic, which they damned well should be. State schools receive about £5,000 - £6,000 per pupil. Some of the most prestigious independent schools charge £35,000 a year, so there would be something seriously wrong if they couldn't provide more. If all state schools received even double what they currently do per pupil, the UK really could have a truly world class education system.