I know this is a silly answer, but I wouldn't start from here.
We have the most socially divided education system in Europe and schools reflect that. The wealthy go to private schools - of varying quality but socially exclusive, the lucky live in an area where there is a mixed catchment area, and the unlucky and the poor live in an area where many schools are described as poor, when the reality is that the intake is from a very deprived area with huge social problems. Again, the schools reflect their intake.
Until we manage to achieve a more equal society and when, as a nation, we are prepared to fund state schools in the same way that Eton, Roedean, Cheltenham Ladies and the rest are funded, no amount of tinkering with catchment areas will make an iota of difference.
And until there is proper provision for children with special needs, whether they be for cognitive difficulties, ASD, or behaviour, schools with a disproportionate number of SEN will continue to be described as poor and parents who can, will avoid them. By fair means or foul.