You've hit the nail on the head, @Zoutdropje .
The primary school previously prioritised (which is how my kid got in) had over two-thirds of pupils eligible for Pupil Premium, which is vastly higher than the national average. The much posher state primary school then courted by Hall, Chappell et al, has about a sixth of pupils eligible for Pupil Premium.
As I said before, about £80 million was spent on the new HPS building, and HPS also has 23,392 sq m of outside space. The new school built to take the kids from the wrong side of the tracks, KAA, cost £26 million, and was built on a sliver of land wrapped around, er, Grenfell, with only 3,881 sq m of outside space - and most of that useable outside space is on the bloody school roof. That said, I wish KAA had been built a couple of years earlier, so my kid could have gone there, instead of spending his school career treated like he was nothing, because he wasn't the "right" demographic.