As above. What does your lease say about parking? What it doesn’t say about parking is equally important. For example, does it mention anywhere that you must display a permit to use your allocated or demised parking space?
Just because some third party ex-clamper puts up some signs does not override the supremacy of your lease.
What exactly did the keeper say to whoever when they appealed or contested it? The NtK is not fully compliant with all the requirements of PoFA and so, the Keeper cannot be liable, only the driver and they have no idea who that is, unless the Keeper blabbed the drivers identity, inadvertently or otherwise.
Don’t worry about a claim issued by Gladstone. They are so utterly incompetent, they will breach CPR 16.4(1)(a) which, besides an easy defence, will get the claim struck out at allocation stage.