London always has had a three tier education at secondary. Private day schools on top, middle classed state schools in the middle and then everywhere else.
Take a typical borough in South East London, Greenwich.
You have Colfe's private day school ( over 30% achieving AAB+ at A level) then good state school Tallis , massively oversubscribed with 12% getting AAB+ at A Level) then schools like Plumstead Manor, still rated good , getting 5% AAB+ at A-level.
This is repeated across every borough across London. There are very few truly 'rubbish' schools in London, given the uplift by the last Labour gov on London schools which has left a legacy of them being well ahead of state schools outside of London.
Within London, even ofsted 'good' schools seem 'bad' , as London has the highest concentration of the best schools in the country. A school like Camden School for Girls, or Mossbourne in Hackney, or Brampton Manor in Newham have A level results private schools outside of London can only dream of. Brampton outperforms Eton currently for Oxbridge places.
The school situation in London is ....complicated. But the 'disconnect' comes from the many tiger middle class parents who use primary state schools as unoffical prep schools in London then enter private at 7+ to prep up for selective secondary