I agree with comments above that the matter is unlikely to become a problem. However, it raises an interesting point.
The school will not contract with a child (ie person under age 18) for contract law reasons. The contract is therefore between the school and the child's parents.
If grandparents transfer funds into one or more bare trusts for grandchildren such a transfers are PETs by the grandparents. Any such monies must be applied by the trustees only for the benefit of the beneficiaries (ie the children).
Should the trustees of the bare trusts transfer monies to the child's parents such transfers constitute PETs by the children. A PET is a gift from one individual (child) to another individual (parent) if the property transferred becomes comprised in the parent's estate (which it would).
Alternatively, if the grandparents transfer monies directly to the school this is not a gift to another individual (and hence not a PET) but constitutes the discharge of the parents' liability to the school and as a consequence the parents estates are increased (because they no longer have a liability to satisfy). This would appear to be a chargeable transfer.
With apologies for re-opening this thread - I was wondering whether payments by the trustees to the child's bank account, from which payments to the school could then be made, would still count as a PET by the child. The child's bank account would be in the parent's name, but designated as belonging to the child. I do appreciate that even if such payments did qualify as PET's, it would be unlikely to be a concern.