https://phys.org/news/2018-07-evidence-grammar-schools-social-mobility.html

In those LAs, the proportion of pupils attending such schools varied widely: from 1.4 to 37.4 per cent. Selection criteria also varied, with pupils in certain LAs needing to achieve more than twice the Key Stage 2 marks of those in other LAs to have any chance of being admitted.

As a result, applying in a different LA—an option more readily available to more affluent families—could increase a child's chances.