A little local difficulty
The implication he draws is that poor children are routinely excluded from their local school, while "richer parents were better at working the system".
This may be true. But his analysis takes no account of urban geography, and the difference between the "local" and the "nearest" school (which is what he actually used).
A typical towncity in England has both higher population density and higher poverty in the centre, and less in the suburbs. The catchment area for a suburban school generally reaches further out into rural areas.
As an illustration, I live on the edge of a city centre, but not in the catchment area for my nearest school (150 metres away towards the suburbs).
My "local" or catchment school is in fact 1km away towards the city centre.
The fact that most people attend their catchment school, not their nearest school, can explain the size of the effect in Burgess's study.
A more geographically nuanced analysis is required to understand the problem, and the simple catchment area system would have to be abolished to overcome it.
Professor Stephen Gorard
Department of Educational Studies, University of York