Am I right thinking your catchment area school has to make space for you if you want your child to go there?
Absolutely not, I'm afraid. "Catchment" is a misnomer, a misconception. They don't have to take anyone within a particular area.
Class sizes are legally restricted to 30 pupils. Schools will take those pupils in strict order of priority. When they are full, that's is, no more spaces.
It starts with children in the care system, then other criteria like having older siblings at the school, having additional needs the school can assist with, faith based (for religious schools), stuff like that.
The final one is closest to the school (as the crow flies). In some years there may be a high number of younger siblings, so the area they take pupils from when those slots are filled may be very small. In a low birth year, the area may be significantly larger.
In my DS1's year there were only 12 siblings out of 60 places. In DS2's year, 28 siblings. Had DS2 not been a younger sibling, he would not have qualified for a place in his school.
FIll all slots with close schools, but the choice for most parts of England is illusionary - you get where you are assigned. The main exception is when you put a less popular school as first choice when an oversubscribed one is your nearest.