There are a few different issues at play.
Whether there will be enough school places is one of those, and thanks to a drop in birth rate it may turn out that overall there are enough (though there may be localised issues/shortages).
However, we can’t tell anything at the moment because the overwhelming majority of private school applicants have always also applied to state schools. So no one was really expecting a massive upturn in application numbers at this stage.
As per PP any “crunch” will come in relation to the acceptance rate, if there is a shift from applicants using state school as a backup to using independent school as a backup and now accepting state school places in greater numbers.
If this happens it won’t be apparent until the first round of continuing interest at the earliest. But really it will take years for the effect to come through as some parents try to keep their kids in private schools until a natural exit point, while others who would have sent their kids private at 4+, 7+, 11+, 13+ or 6th form now no longer do so.
“There might be enough school places” also isn’t an answer for the massive disruption that this will cause to those families who do have to pull their kids out of indies, especially those halfway through exam courses and those with SEND.
Nor does it support the (ha ha) rationale for this policy of raising funds to improve state education. Every child that moves to state (or who doesn’t go to indie after all) ends up costing the public purse. Any SEND kids moving over will cause already very thin SEND provision to be stretched even further.
So the policy could end up causing a net drain on public finances. But we may struggle to find out as for some reason the government is not attempting to collect the relevant data…🧐