As xabiachica says, you definitely have the freedom to choose to APPLY for a place in a different school, but it depends if they have a full intake that year or not. And it depends... who you are dealing with, and if they are sympathetic or not. If you are just a bit outside the catchment area, that should make a difference too, well in theory.
I know when my son was at state nursery school, and I was trying to get a place in a different one (the one opposite my house!) it was mega complicated . Both had massive waiting lists, and once he got a place in the first one, they said I could only apply to change to the second one at a certain time of year (before February or something) and even then I had to have different circumstances (ie new address - even though I couldnt actually get any closer to the nursery without moving in there), and I already worked 5 minutes away.
So I had to wait till the following year to apply, which they then said was impossible because I couldnt apply for another nursery place in a Junta de Andalucia nursery if he was already down on their computer as having one - I only wanted one, it wasnt like I was being greedy! lol.
In the end, after much lobbying (I kid you not), a way was miraculously found to bypass all this bureaucracy, and I cant even explain to you how stressful this whole experience was, but he did finally get in.
Having said all that, I think the schools process was easier in some ways, though they did not correctly award the points that they should have done (and I have been in dispute with the Junta over that too for about a year and a half, although they have now given me some of the points). I also know of some parents who couldnt get their child (aged 6) into the school which was in their catchment area!
I have heard that when it comes to schools, like a lot of things here, it makes a difference if you have a personal connection (enchufe) with the school. If not, try to make one (before you make the appointment)! If you know of any parents, preferably Spanish, with children there, they might be a help. Or at least try to find out who is a sympathetic soul there, and approach them (whilst smiling sweetly!).
Wish you luck on this one.
Caz. I