Dave is indeed right
Whilst the legal duty to ensure that every child who is of compulsory education age residing within the LA boundary has a place within a school rests with that LA, since the coalition government the LA is prohibited from opening new schools, if they need to provide places there are limited options open to them.
The can extend an existing school - those who are familiar with the geography of the area will know that this isn't really a solution.
A free school could be established, sponsored by big business or another Academy Chain - many have been established and many have failed, it has wasted billions in education funding.
or, as in Kent a school could establish a satellite campus - although I imagine this route is reserved for Grammars only.
The Gove approach to education has been a disaster and very few have really understood what it has meant, essentially market forces, privatization, faux competition, forced academisation and the removal of any democracy. All under the umbrella of 'rigor' and school improvement. However, as Ofsted and the DfE have just confirmed, schools that become Academies are more likely to remain inadequate 1
So, the only Academy near by, Mellor Primary, with the help of the LA was 'Outstanding', now it is 'Good' and has no support from the LA as it opted out, so faces the prospect of being sponsored if deemed to be coasting, or, spending vast sums of cash on consultants to make it improve, Ludworth on the other hand has been and remains Outstanding and Rose Hill is steadily improving.
As a parent my real concern is that we are fast moving to a US model of standardised tests, a focus on what can be measured rather than what children need to stimulate their minds.
1
https://www.tes.com/news/school-news/breaking-news/schools-become-sponsored-academies-are-more-likely-stay-inadequate