Looks like the treasury has just confirmed that VAT will be payable on school fees relating to next January’s term onwards - but not for those who have prepaid before today who will not pay VAT.
However it is also said that the government stands ready to challenge lump sums paid in advance where the fees have not yet been determined.
https://assets.publishing.service.gov.uk/media/66a7a1bdce1fd0da7b592eb6/TechnicalNote-_DIGITAL.pdf