This school's supplementary form clearly states at the top of the form that you are required to complete the local authority form and that the supplementary form is not an application for a place. The school clearly states in the admission arrangements on its website that you must apply through your local authority. The local authority clearly states in multiple places on its website that you must apply through the local authority if you want a place at this school.
I understand that you are upset. I understand that you feel the school and local authority have let you down. But I'm afraid they haven't. They have both gone beyond the minimum required to make sure you knew how to apply. Even if the school's form was the only document you read, it told you that you needed to apply to the local authority. The school's staff were not required to prompt you to apply to the local authority and had no reason to do so. After all, you had submitted a form that told you what you had to do.
I'm sorry but, however much you might want it to be otherwise, no appeal panel will accept that either the school or the local authority is in any way to blame for your failure to apply on time. They will take the same view as people on this thread. It was up to you to apply on time. There was more than enough information available to you telling you what you had to do. The late application is therefore entirely down to you and does not provide any reason for an appeal to succeed.
As you are first on the waiting list you will almost certainly get a place. As you say, it is not guaranteed. But I would be very surprised if there is no movement at all between now and Christmas.
if a family moves to the area halfway through a school year they have to be given a school place and then there is 31
That would only happen if there were no schools with places available within a reasonable distance from home. The child would then be counted as "excepted" under the infant class size rules, which means they don't count towards the class size limit. As you haven't moved into the area but are just a late applicant your child is not excepted. If the school admitted your child they would be breaking the law on infant class sizes.
Cut off points are fair when you are aware of them. We were not aware
The school and the LA did everything they are required to do and more to make sure you were aware. It is clear that you completed a form that told you what to do. Hundreds of other parents got it right. I'm afraid it is your own fault you were not aware. The cut off point is perfectly fair. What would not be fair would be to treat you equally with those who applied on time.
With this extra information provided, is there is still no chance of winning an appeal?
No chance whatsoever, I'm afraid.
I know the above isn't what you want to hear. But it is how things are.