Proximity Charges
This situation exists for one main official reason: primary school students are assumed to be helped by being assigned to a school that is nearby. Can't really argue with that, can you? It is certainly much more convenient for a child if school is next door.
However, schools are not evenly distributed according to geography, both human and physical. Of these two factors, the latter is somewhat less controversial: yes, maybe school is across a rivulet or a canal, or up a hill – but this country's lack of outstanding physical barriers does not usually create big problems. The human factor is more troubling. There is a direct link between socioeconomic status and school achievement, and it is quite clear that many of the country's premier primary schools are right smack in the middle of juicy real estate.
It is clear that more wealthy households can in general afford better educational support, so a school in a wealthy area tends to benefit from better-supported students and parents with greater resources. School achievement goes up, the school appears more desirable, and property values around the school also rise. The cycle feeds itself.
There is a way to make the cycle a little less lethal though. The country has about 180 primary schools, of which perhaps 20 are greatly in demand. A simple tweak might help. Why not remove the distance bonus for schools in the top 20? Give schools a ranking coefficient over 5 years; this is certainly not beyond the powers that be. For schools in the top 20, the barrier to 'immigration' will be removed, thus allowing them to be accessed by anyone willing to travel a greater distance. This allows children for less wealthy backgrounds to chance, without undue penalty, an application to a top school.
This means that a headache will be created at such schools. Never fear, it is one that comes only with success. If you are a successful school, you will have to allow random chance to dictate your population. And if you are really a good school, it shouldn't matter what kind of students you get. So schools in swanky districts with excellent results will have a better mix of students, and the same goes for schools in poorer districts with excellent results. Joy all round, I suppose.