A parent has complained that my report persuaded another school not to admit her child. Surely I have simply done my duty?
You probably have. It is a legal requirement that a school should provide information about a pupil's scholastic record to a school where the pupil is seeking admission.
The law does not oblige you to provide character references, nor to offer opinions beyond te basic facts of academic attainment. Like you, however, most heads would regard it as a proper professional task to provide as much objective information as they have both to assist the other school and to serve the best interests of the pupil.
The parent is, in any case, entitled to see whatever is contained in her son or daughter's file and to challenge any factual error.