There is absolutely nothing in law to prevent the headteacher of the current school from supporting an appeal.
However, some Local Authorities or governing bodies might instruct their headteachers not to get involved.
To be honest, I don't see the value of a character reference for appeal purposes.
If you're appealing because of non-qualification, the evidence should relate strictly to academic ability or extenuating circumstances.
See:http://www.elevenplusexams.co.uk/appeal ... cation#b20
If you're appealing because of oversubscription, it helps to have evidence that supports any of your reasons for wanting a place at the school being appealed for (e.g. the child has a particular aptitude for the subject that the secondary school specialises in).