A "non refundable admin charge (not 'fee')" is a penalty and therefore unsustainable and if you took the landlord to court you would probably get your money back if he refused your request. You are only liable for "reasonable administration costs" and only if the landlord states this in terms on which a property is reserved. A court will expect the landlord to be able to itemise his actual costs in order for the court to award anything to him.
The advice I give should not be construed as a definitive answer, and is without prejudice or liability. You are advised to consult a specialist solicitor or other person of equal legal standing.