Several posters are missing the point. It is far too soon to tell and current data is going to show no change. The government have also deliberately applied this in a way where it becomes very difficult to see any negative impact in the short term
There are a group of parents who choose private education as the default and their children will remain in the sector regardless of VAT. They can comfortably afford the fees, 20% is not really that much in the grand scheme for them.
The other group (like myself) are those that have chosen private for a specific reason with no commitment to remain in the sector throughout their child's education. A lot of parents at my DC small prep school fit into this category - we have chosen this school because of lower fees compared to through schools and wanted our options open. We can afford the fees but make noticeable sacrifices to do so and 20% hike is significant. The majority can make changes to their finances to fund the VAT until the next natural breakpoint - I only know of two children leaving the school mid way through primary due to VAT and they are still staying until the end of the academic year.
In our school, the trend previously was for these parents to eventually choose private secondary because of career advancements making secondary fees an option with the same level of sacrifice. Historically, around 10% have moved into state sector but these parents all apply for state secondaries and always have done. We are certainly seeing change as 40-60% are now switching sector. A few current Y6 moved house within the past 18 months specifically to be in catchment for particular schools, 5 families (and counting) have done this in my DC Y4 group.
There are also those who are currently in state primaries with the intention of moving into the private sector. They also will likely be applying for a state place.
So from what I can see, the net impact and allocation on state places last week will remain similar. Some who are in private and have moved into catchment will get places on distance so there has been changes in catchments of some schools but there could be other explanations - we can only speculate when the government refuse to collect data.
As a PP said, the VAT policy is not going to have a major catastrophic impact on the education sector. In our area, the competition for the higher performing schools has increased and will likely stay at this level or increase further.
There are enough state places for every child in the country, there is no disputing it. I predict some on the outer edges of catchments of popular schools are going to lose out on their school of choice in years to come as more switch sector/never start private. The bigger question is whether the VAT raised will actually offset when factoring in the cost of educating those that switch/never start private education and the cost of SEN provision that is going to be needed for those who have now been priced out of the sector. If ends up costing more (which is my prediction for the long term), what was the point in the policy?