I think the VAT that is not paid is fairly neatly offset by the money saved by the state on not having to educate those 620,000 children.
Over 15% of children at private schools have special educational needs and the data suggests that increasing numbers of parents have made a difficult financial choice to go private because they know their children won't get the support they need at a state school. By contrast, kids with SEN at state are dropping, which suggests they're either going private in despair, or not being diagnosed any more (or a bit of both). Neither answer is particularly encouraging.
www.schoolmanagementplus.com/inclusion/matt-hancock-calls-for-dyslexia-screening-in-primary-schools/
Do state schools across the UK actually have the facilities to take on an influx of kids from the private sector - including a slightly disproportionately high number with special educational needs? Kids with autism who are in a small private school setting now and thriving, but who will fall apart in a bustling large state school? Kids with ADHD, dyslexia and all the other things that need smaller class sizes?
I do take the point that if more affluent and ambitious parents were funnelled towards the state system instead of being able to buy their way out, it MIGHT uplift the state standards/budget/outcomes, but I think it would put many local schools under a lot of pressure to suddenly have to accommodate hundreds more local children.
I do feel that the value of the VAT is offset by not taking a state place, but if VAT MUST be introduced, it should be phased in so that borderline parents (who represent the VAST majority of parents that I know who send their children private) have time to adjust, especially at points along the way where teens have chosen A-Level subjects that their local state school might not be able to accommodate - and the state schools to find the places for them.
Also... show me a head teacher in the state sector who is blissfully happy with her budget and is excited about taking on more teachers next year to offer a wider range of subjects for A Level, and get her class sizes down to 20 for Year 7. Who has all the money she needs for sport, art, music, and SEN. And to repair that hole in the roof and fix the toilets without having to choose between basic repairs and TA's.
That's why people who can, go private. If the Labour government actually funds education well enough to provide schools with the budget they NEED, you'd find more parents switching back to state with great relief, without needing to be "punished" with VAT.