Government guidance says that your child should only have been excluded:
Government Guidance is contained in a document called “Exclusion from maintained schools, Academies and Pupil Referral Units in England”
‘It is unlawful to exclude or to increase the severity of an exclusion for a non-disciplinary reason. For example, it would be unlawful to exclude a pupil simply because they have additional needs or a disability that the school feels it is unable to meet, or for a reason such as: academic attainment / ability; the action of a pupil’s parents; or the failure of a pupil to meet specific conditions before they are reinstated. Pupils who repeatedly disobey their teachers’ academic instructions could, however, be subject to exclusion.’ Exclusion from maintained schools, Academies and pupil referral units in England – June 2012 paragraph 12.
Your child can be excluded for behaviour outside school if the headteacher feels that there is a clear link between that behaviour and maintaining good behaviour within the school.
Only headteachers (or the nominated member of staff in their absence) have the authority to exclude a pupil. The headteacher should not exclude your child in the heat of the moment, unless there was an immediate threat to the safety of your child or others in the school.
The headteacher may exclude your child if they feel that on 'the balance of probabilities’ they did what they are accused of. The more serious the behaviour your child is accused of, the stronger the evidence against them needs to be.
Before deciding to exclude your child the headteacher should: