Are you happy to talk to your current school about this? I think you need to ask them what evidence they sent BCC (I assume it's Buckinghamshire?), and whether they supported your application. (Sometimes BCC will overrule a headteacher's support, if they think that the evidence does not back it up - but this could possibly weaken the authority's case at an appeal.)
You could then go on to ask the school for a copy of their report (pointing out that you will get to see it anyway if you go to appeal, but it would help you to prepare your case now).
An appeal "to test" is usually simpler than an 11+ appeal.
Evidence that you present might include some of the following:
*Above average KS1 results (although they are starting to look rather ancient
*A reasonable 11+ result
*Two level 5s at KS2
*Good predictions for KS3 (although it may be too early for these to be available)
*Any recent good school reports (especially if there is reference to high achievement)
*Results of any standardised tests (the higher, the better)
*Support from the current school
Do ask if you have any further questions.