My understanding is that schools can cap students based on individual risk assessments- e.g. if they do not have the staff available due to self isolation etc, they cannot have all the students in that they usually would.
The school will also have individual risk assessments around social distancing etc.
If all work is being set online, some schools may be practically limited by access to IT and feel the need to prioritise.
It is a really difficult situation, and just because the government guidance says something should be in place does not mean it is always practical or possible to offer.
That said, it does seem to me that your son ought to be offered a place. It sounds like, even with their published criteria, places were offered on a first come/first serve basis, the school have hit capacity and they now can't offer your son a place without refusing someone else- which would be very tricky to do. And it's easy to say that one extra child wouldn't be an issue, but I bet you aren't the only one asking for a place.
I hope you do manage to get somewhere with the school and I think it's entirely reasonable to be angry, but unfortunately, I think you also need to think about plan B.