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.
I think this is entirely analogous to giving priority to siblings of existing students. Cuts down on unnecessary journeys across the borough, simplifies childcare arrangements but also good for staff welfare and management at schools.
It would surely be better to focus on the "serious shortage" than make the lot of inner city teachers even harder than it already is.