There is no real alternative and lots of reasons to go to this school (integration into village, school bus provided, only primary in DTA, similar size to current school).
Therein lies the basis for your appeal.
When you receive the school's case for prejudice you will have a better idea about what you are up against. You should be able to see whether the school as a whole is up to its capacity, whether this or any other classes have extra children in them, what restrictions on numbers are placed by room sizes etc.
The LA don't often consider that there is "no real alternative" (especially as they will offer transport to the nearest available school with places as long as it is over two miles away) but if they do they would approach the school to ask it to go over numbers.