The legal position is set out in the CoP:
The panel may then need to consider any clear evidence presented by the appellants to support their claim that the child is of the required academic standard e.g. school reports giving Year 5/Year 6 SAT results or a letter of support from their current or previous school clearly indicating why the child is considered to be of grammar school ability. The panel must not devise its own methods to assess suitability for a grammar school place unrelated to the evidence provided for the hearing. In determining to uphold an appeal, the panel must be satisfied that there is evidence to demonstrate that the child is of grammar school ability and, where applicable, that the appellant’s arguments outweigh the admission authority’s case that admission of additional children would cause prejudice.
The decision whether a child is considered to be of grammar school ability must be based on evidence, and the 11+ results, of course, form part of that evidence.
If the child is as bright as parents say, it inevitably raises the question 'Well, why didn't he or she pass?'. This is why extenuating circumstances are likely to be a relevant consideration, except perhaps in very borderline cases.