Etienne, would you say that straight level 5's, a head teachers wholehearted recommendation & a good solid pre-test pass (an official test) demonstrates high academic ability?
It would be a good starting point, if the aim were to establish grammar school ability - although appeal panels in selective areas know there is a lack of consistency in headteacher recommendations (i.e. some heads are over generous, some may be too strict).
If I've understood correctly, you don't need to prove grammar school ability, although - depending on what sort of case you feel able to put forward - you might wish to try and demonstrate that a higher score could have been expected. It depends which areas of the 11+ showed a relative weakness. If in VR, then an appellant with several exceptionally good CAT or NFER verbal reasoning scores (e.g. at the 95th percentile), or a similar standard in an educational psychologist's test, would have alternative evidence for the panel to consider. If in maths, then a 5a prediction, and a supportive statement from the headteacher (e.g. "gifted & talented, best maths student in a high performing school, entered for level 6
") might be well-placed to try and argue that the 11+ result was a blip and not a fair reflection of ability.
Where score is one of the oversubscription criteria, and if there are a lot of appellants, then I would imagine the more compelling the case would need to be (in terms of academic evidence and/or reasons for wanting a place). Ultimately, though, it's a decision for the individual panel.