Some schools will always close, as I evidenced. Yes, some are small and some are religious, but plenty of perfectly ordinary private schools close every year.
I know of one on Chelsea, thought there was a niche and more demand than there was. Opened, couldn’t fill itself, closed about 3 years later.
Demographics change, new schools open in competition, fashions change in mixed vs co-ed and schools are no longer in demand. And of, course bad results can easily be the demise of a private school.
Yes, VAT will cause some additional schools to close and, on a population level (not a pupil or parent level), this is not a disaster.
There is also plenty of economies to be made in the vast majority of private school to keep them viable. People will keep saying this isn’t the case, but if a state school can manage on £8k per pupil (secondary) a private school which charges 2-5x that amount can economise.