dobbin1
Presumably you meant to say Examiner.
It's entirely plausible that an Examiner might have a business that is VAT registered but carries out his Examining duties separately and on a self employed basis, in which case he would not be allowed to add VAT. This is commonly the case where the Examiner owns the school.
If a school did not make an admin charge for passing on the fee they could not charge VAT on that fee. If they did make an admin charge they could only add VAT to the admin charge, not the fee.
However, it is still the case that the fee should be charged by and paid directly to the Examiner.