Indeed, Haybott.
This is a teacher friend's LEA:
A defunct secondary school which closed due to falling numbers could be resurrected as early as 2019. Education chiefs have disclosed that the Chaucer Technology site in Canterbury is their preferred option for a new secondary serving the city as the population swells.
Chaucer pupils left classes for the final time in June last year following Kent County Council’s decision to shut the school as it was “no longer viable”. The closure is already putting strain on other secondaries in the district to absorb additional pupils.
KCC now says it favours two new free schools – a form of academy funded by government but free from local authority control – one in Canterbury, one in Thanet. (Kent Online, 1 Aug 1916)
So there isn't capacity for the existing students after this closure, and central government prevents the LEA from just opening a new school: it has to wait for someone else to do so.
And friend left the last primary she taught at in the same area also under threat of closure, also for falling rolls.
Now this is an area with about 12% population growth since the 2001 census, so the situation is only going to get worse. I don't know how much of the growth is from foreign immigration (possibly not much), but for anyone so inclined, it makes an attractive and simple story to say immigrants are responsible for lack of school places. It just isn't actually true.
In friend's area, immigration hasn't caused the problem. Stopping immigration can't fix it. But blaming immigration is a nice diversion from the idealogical political decisions that are the real cause.