I have also put this in the law section but wanted to know if a techer gives a child a detention and a parent specifically says that they do not give permission for their child to be kept behind for very valid reasons can the teacher legally keep the child behind at school?
No the school cannot keep your child behind without your prior permittion. All detentions require a minimum of 24hours notice and a parent/guardian being informed via phone, writing or detention slip.
You are totally within your right to refuse although if the problem for which your child received the detention persists your school will be well within their right to exclude from lessons etc.
A school must give notification but they are not requesting permission by doing this, merely informing so therefore permission is not required so the child can be kept. As I suggested on the other thread though, most would rearrange if given a reasonable request.