If you don’t have the Notice to Keeper then you have time to obtain it by submitting a Subject Access Request to Smart Parking for all the personal data they hold on you. It won’t be soon enough for the reply to the LoC, but it will be soon enough to be used for the county court defence in due course.
From re-reading this thread, you overstayed for 15 minutes and Smart will say that they operate a standard 10 minute “grace period” which allows for overstays, but you exceeded it. Without the original NtK it’s hard to tell if it fails, but don’t identify the driver in anything you write, you are the registered keeper, and when we see the NtK in due course there’s a good change that it fails the requirements of the Protection of Freedoms Act 2012 to transfer liability from the unknown driver to the registered keeper.
