OK then, let's do the maffs. I'm using example figures, rather than the specific amount being funded via GAG, as this varies at key stage, level of deprivation and location (plus many other factors in the NFF). The minimum amount for 2023-24 was a smidge under £6k per pupil.
1000 parents of children at private school paying £20k annually.
VAT comes in for September 2025. They therefore need to pay £24000. This would represent 1000 x £4000 = £4,000,000
10 of those parents move to state instead (1%). The tax received is therefore 990 x £4,000 = £3,960,000
The amount paid per child is (just under) £6000. They therefore cost the DfE £60,000 to educate in a standard school.
Net gain from introducing VAT is therefore £3,960,00 - £60,000 = £3,900,000.
If 10% leave (so 100 children), that's 900 x £4000 = £3,600,000.
The amount paid is £6000. They therefore cost the DfE £600,000 to educate in a standard school.
The Government's still three mil up on the deal, as they're getting a net of £3,600,000 - £600,000 = £3,000,000.