They are relying on people going private. If they did not, there simply would not be enough places for the numbers of children, even if some of them were hived off to schools they had not applied for. What do you think would happen to the many people who currently do not have a place at all?
We have accepted a place at a private school, even though DD got into Tiffin and would have definitely got Christ's if we hadn't applied to Tiffin - so two perfectly good state schools. One of the reasons we have done so is that I am sick of the government playing politics with children's education. I am sick of the pressure to get results and progress. I am sick of Ofsted which I don't think is doing a good job and I am horrified by the focus on SATs we've seen this year, at what is mainly quite a nurturing and child-centred school. I don't like the chopping and changing of the curriculum and I don't like the EBacc. I could go on.
Many of the schools we have around here are good and the same goes for lots of the local private schools. I don't think that people going private is only because they don't get a place at a reasonably good state school, I really don't.
A parent in Sheen would be very unlikely to get their child into a school in Isleworth or Wandsworth this year, IMO, and it will get worse. We are just starting to see the bulge in birth rates coming through to secondary level.