If Labour wants to eventually end parents buying privilege through private schools, it needs to go after school catchments. How can it be fair to decide schools by distance to gates when it often depends on ability to pay rent or mortgage which will usually be higher in catchment for good schools?
The only fair system is a lottery one by borough (at least for secondary when kids are old enough to travel alone). You should be allocated a place within your borough but it should be randomized and not based on distance to gates.