The very very small numbers of private school pupils will be very welcome at state schools. It will absolutely not be a problem- there are spaces at state schools. Nobody knows anything about how many pupils will move. The most optimistic semi-formed estimate is from the IFS, who say 20-40,000. other estimates say up to 135,000. Nobody really has a clue.
It's flat out untrue that there are places at state schools. Not only are some schools full and oversubscribed, there are boroughs and even counties where they struggle to accommodate even one home-mover, let alone give them a choice. And nobody, even the rather optimistic IFS, claims to predict where pupil migration will happen or how it maps to state school capacity.
Having motivated children and parents at state schools can only drive up the progress of state schools. It will be a good thing for private school pupils to move to state schools. Can you explain precisely how this works? Do you have any evidence? Do "motivated children and parents" drive up the progress of state schools today, or do they buy catchment areas and tutoring? do you assume affluent ex-private school families will behave differently to affluent state school families?
Private school parents are welcome to spend their money on tutors, I believe a lot already do despite being in private schools. It will make no difference at all to children already in state schools, it will not disadvantage them any further than they already are in comparison to private school pupils. Now this makes sense! Affluent families will continue to buy better education, it will continue to do no harm to other children. But it won't raise VAT revenue, it will mean they demand those unfunded non-existent state school places, and it will give those higher earners the opportunity to consider whether they need to work so hard and pay so much tax to pay for the education of others.