I take it the head's view is that there's no chance at Herschel, so no point appealing. I think that the only justification for refusing should be that there's not enough evidence to support an appeal. Unfortunately there's no easy way of obliging the head to co-operate. You could consider kicking up a fuss, but it might be wise to wait until after the Bucks appeal.
The issue of unco-operative heads is discussed in the appeal Q&As (B20) - but in the context of opposition to selection.
You could probably use the support that the head gives for Bucks, although it would mean revealing that you have appealed elsewhere.