@Walkaround - regarding London primary schools, the oversubscribed sought after ones are fine. In fact, people chase them even more.
Where I live there are 2 really successful church schools, one COE and one RC. They have just made their criteria less stringent, for example, COE used to be 3 years church attendance, has changed to “practising Christian”. The locals are delighted.
When my children were mid primary there was a huge baby boom and lots of schools expanded their entries from 2-4 forms, as an example. Kids were allocated primaries miles away and didn’t get any choices. Most eventually got places locally in year 2/3 etc some left London because of it.
That trend has simply reversed and the powers to be should have planned for it, they have the Census data and knew how many children are being born and leaving London. Just like they didn’t plan back with my children were younger. Very slow to get into gear in this country. Obviously a small school that cannot fill its roll is a sad state of affairs and the Government should plan appropriately and give the right bridging funding. A lot of the issues are to do with per pupil funding.
When there is a “crisis” in state and private education what actually happens is that the most sought after schools becoming even more so. This applies to pupils, parents and teachers. Teachers tend to also want to teach in thriving, successful schools and note that many state schools now also give priority to the children of teaching staff.
Even with SEN in a thriving privilieged school the parents of SEN children are more able to fight for the EHCPs, pay for a private diagnosis in time, are not in denial/scared of labels, want to get all the help they can get and work with the schools from the start. A lot of it is to do with faith in authorities and the system. A good head helps too.