There isn't really a shortage of school places at that end of Dartmouth Road. The expansion of Kelvin Grove as well as three other local primaries (including two church schools) means this is not the best choice of sites for a new primary (not that I would oppose any such plans).
Additionally the council owned depot on the other side of Willow Way will become temporary space for a Sydenham school that is being rebuilt.
The police station does not belong to the council but belongs to the police. The police station in East Dulwich was recently sold off, possibly for a new primary school.
What I don't understand is why children of teachers should have priority on waiting lists above other children who live closer to a school. If we didn't have a serious shortage of places then it might be more reasonable, but when there are some areas of SE23 where you are unlikely to get into the three closest (non-religious) schools, I don't think allowing others to jump the queue will be popular except with teachers and the Independent schools sector.