Staff are often asked to sign applications for passports on behalf of children. It is something many teachers are happy to do in their own time if they feel it is appropriate. Parents are asked to take into account how busy teachers are and allow a few days for the forms to be completed.
If the teacher has agreed to sign an application, the teacher is confirming that they know the parent not the child. If the teacher has not personally known you for the required amount of time they will be unable to complete the form.
A donation of £10 towards school funds would be appreciated for each passport application.