Then no. They can not charge it.
They can only levy a charge if the contract says they can.
Really it is down to poor drafting.
It should have said that permission would be granted, not unreasonably withheld and the Landlord is entitled to charge a reasonable legal fee.
They did not
Therefore they can not charge it.
They can not change the terms of contract after it has been signed.
Can I clarify anything for you about this today please?