Callistemon I'd forgotten you're in Wales. Sorry!
In England, everybody has the right to apply for a school in any authority. Academy chains are their own admissions authorities. Distance is usually one admissions criterion, but there may be others, such as siblings, musical ability or religious affiliation, which might trump the distance. Authorities aren't obliged to pay bus fares to a school outside the authority, if there's a closer school, which puts some parents off.
It's estimated that about 12% of available places in England are not filled, while some schools are over capacity - that's a planning decision at local level. Primary demand is about to dip and secondary demand will follow in about 3/4 years. No authority will build permanent places, when they're only needed for a few years.
Education authorities usually publish forward planning predictions with the predicted number of places needed for up to 10 years. Usually, there are enough places in total, but most authorities have "sink" schools which parents don't want. Authorities won't commit to new building unless the surplus numbers are in multiples of 30 (a class) and government regulations state that new schools can't be built unless there's an established need, which is why schools won't be built until houses are occupied and every surplus place is filled. Groups of parents can get round that using the "free schools" initiative, if (for example) they can show that there's a need for a religious school or one for pupils with special needs, but it's a long process.