No, not like for like, but the point is (one of the points, perhaps) is that inner London does present a model where there cannot be a house-price ghetto because within 50m of ordinary yet ludicrously expensive terrace houses or 20s semis there will be a high density council estate. And in the density of London housing there will be a high ratio of social housing. (perhaps this accounts for the high average spend per capita?) and I live in a borough with very high overall levels of deprivation.
Within this model it is the case that in schools with a very mixed demography can be very high achieving. Good schools. Despite having many of the families LaQueen etc wish to avoid. So why in suburban areas to people flock to avoid schools where there is more of a mix of pupils? Thus creating more of a polarisation? And driving house prices up?
Even in catchments where the intake is almost exclusively from highly disadvantaged housing, the schools and the results can be very good. Look at Platanos college, formerly the feared Stockwell park School. And house prices do not correlate to school desirability: house prices in Brixton are way more expensive than in Streatham or Lewisham , but the schools in Streatham and comparable areas of Lewisham are far more sought after and oversubscribed than the Brixton secondary.
The model of schooling within mixed ability, and a hugely mixed demography, and achieving good results for all, is successful in London. And could be elsewhere. But people fear it, and move to an expensive catchment, or seek selective schooling.
Not all schools in S London are good or desirable, of course. But that isn't inherently due to the mix of pupils.