Sunset that sounds like some seriously bad planning on the part of your LA.
It's one of the idiocies caused by having 2 tiers of local government in "shire counties", Barbarian.
The district council gives planning permission for 1,500 houses, the county council fails to expand the schools to fit the increased population. They may even need DFE approval to do this, they certainly do to build a new school.
SE news had a story the other night about people forced to send primary age kids to schools 6 miles away, because a big housing estate had been built on the edge of town. They couldn't get their kids into any of the schools in the town, I think there were 3 or 4 primaries.
It's happening where I live too. The LEA added a "bulge class" to a school on one edge of town a few years ago, rather than add a few children above PAN to each of the 5 schools. All the siblings of the "bulge class" kids are now schlepping across town to that school, while loads of new houses have been built close by (literally adjoining the school site, in many cases) and the people who have moved in are schlepping their kids across town in the opposite direction.
God knows how many extra car journeys that blindingly brilliant bit of joined-up thinking has caused. The whole bloody town is gridlocked for 30 minutes twice a day, as they all crawl round the one-way system.
It's bonkers and I feel really sorry for parents.