Is the head saying "It's too late now that you've submitted your appeal," or "The appeal system doesn't allow it," or "My LEA/governors won't let me do it".
What you are asking for certainly happens elsewhere. In Buckinghamshire, for example, heads provide an up to date report on English, Maths, and Science, predicted KS2 levels, and a statement of support. Year 6 teachers sometimes write their own letter of support.
Whether this information can technically be presented as late as the day of the appeal is not crystal clear. The Code of Practice says:
Parents should also be informed that there is no statutory time limit for submitting information about their appeal, and that they may be able to submit information after lodging their appeal, but before the hearing. However, it then goes on to say: There should be no grounds for the admission authority to produce substantial new information at the appeal, although this should not be true of parents …….
It might be worth checking with whoever is organising your appeal to see if they have a view about this, but in practice, I’ve never heard of parents being denied the opportunity to submit additional information after lodging their appeal. As far as the day of the hearing is concerned, if you were to turn up with six copies of some strong new academic evidence that you had only just received, I think the panel would be wise either to accept it or to ask for an adjournment to have time to consider it. Otherwise I believe you could have grounds for a complaint to the ombudsman.
Now, to return to the head, it depends what he means when he says “this is not the procedure and he is not allowed”. From the point of view of the appeal procedure, I can’t really see anything that stops him from providing a report. If what he’s saying is “My Local Authority (or my governors) won’t allow me to help you because they’re opposed to selective education”, that’s another matter, and there’s probably not much you can do about it. Ask him to put his reasons in writing, so that you can show them to the appeal panel.
If the head won’t co-operate, have a private word with the classteacher to see if he/she can do anything to help. (This obviously puts the classteacher in a difficult position, but the worst they can do is say “No”.)
As an alternative, you could also consider getting an assessment of your child’s ability from an educational psychologist (money and time permitting!).