14 days only applies if they want to hold the registered keeper liable rather than the driver, so you reply along the lines that they can’t hold you, the registered keeper, liable and to take it up with the driver, who you will not be naming.
If they come up with some malarkey about not using PoFA and assuming the keeper to be the driver, you just laugh at them.
They know that lots of people will just pay up, and it looks like you’re not one of them.
In due course they’ll likely reject any appeal but send a POPLA code who will most likely rule in your favour when you appeal to them.