"holy city privilege"
Both mine were offered state secondaries at least three changes of bus/tube. DS was only offered a place in May and would have had to travel through two boroughs to get there. DD did not get her nearest school. Gove, Cameron and Adonis did, as did the DDs of several senior Labour politicians.
In fairness SPGS do give a fair number of 100% bursaries, and in London private schools this can often mean help with Uniform, school trips and so on. However I am not sure I would send a child there. DD knew quite a number of her peers via extra curricular activities, and almost without exception they were members of the Chelsea/Kensington/NottingHill/Belgravia international banquier elite. I think some pps have it wrong in their class analysis. Top British schools are very very international, and to a noticeable extent there is a social divide between the international rich and the British. Indeed DD once asked, aged about 12, why others were allowed to be so racist against the English. If you were not at SPGS you had to be stupid, despite the fact DD often helped others complete their homework. (There is little evidence that teaching, especially maths, at SPGS was better than elsewhere.) And if you were not aiming for a top US University, you were clearly deficient in the brains department.
The level of arrogance was stupendous, as was the assumption that "my child" came first. One mother once bent my ear about the unfairness of taxing non-doms. She did not understand that perhaps she should be contributing towards a country she had lived in for well over a decade. A bit older, and DD described it as toxic. She also said that one of her friends openly admitted that his parents voted Trump. Yes the man was a clown but he was more likely to help protect the wealth of the very rich.
So a baked potato is weird. But it is a start. Those kids, once they have completed their expensive Ivy educations will be running firms like Amazon, Goldman Sachs and Google. Perhaps they should know that the poor exist.