Most independent schools operate with narrow margins, and there isn't much "cloth to cut". The threat (and implementation) of a 20% tax adds to these challenges by pricing some families out. Schools like these can't afford to lose too many students, which means this pressure was too much to bear. VAT is acceirating the loss of pupils.
IFS said 2-3pc margins. The governments position was that schools can absorb VAT (plus business rates, NMW and NI) but never saw fit to explain how. Reality: either parents, or jobs, take the hit, or the school closes.
Previous school closures were smaller, more recent types and balanced by openings. The volume of closures of larger, long established schools is unprecedented.