I presume your school’s PAN is 30?
This means that when a parent applies for a place (other than in Reception) they will be told the school is full, and they will have to appeal for a place. They may also be offered a place at a different (almost certainly unpopular / less well regarded) school, if one has places.
When the appeal is held, the panel (for KS2) will be balancing the prejudice to the school of taking that additional pupil vs the prejudice to the child of not being admitted to that particular school.
Where there are multiple appeals for the same school, if the panel finds that there is space for eg 1 extra child but not 6, they will decide which child has the best case for admission.
If a child is at risk of having no school place at all within a reasonable distance (note - not no school place of their choice: if a place is available in a ‘very much non-preferred school’ then it is that place they will be offered) then the Fair Access Protocol can be invoked, where a school is directed to take the child. Note that the school directed to take the child is NOT of the parents’ choice: it is the one judged to have the most capacity to absorb the extra child).
If your child’s school has classes of 30, this may be evidence of a relatively static population, where most children start at Reception and few leave ir join going up the school. Or it may be that it has small classrooms or very small corridors or a small hall that means they have successfully defended the class size at appeal (ie the prejudice to the child has had to be unusually high to overcome the significant prejuduce to the school).
I have worked in an area where KS2 appeals were extremely common, as families moved into the catchment for a secondary. Different schools maintained different class sizes despite multiple appeals to all; one of 30, one of 32, one of 31. None went higher except in unusual circumstances (a bulge of 33 due to twins, for example). Children were often allocated instead to somewhat more distant but still reachable schools.
The private school parents who think they will automatically get a state school
place of their choice are due an appeal-filled set of surprises, I fear.