It doesn't matter what the sigs say. What your lease/AST says about parking is what is important. What it doesn't say about parking is equally important. Just because some unregulated privater parking company puts up some signs because the management company has contracted them, does not override your supremacy of contract.
For, example, if your lease makes no mention of retiring a permit to be able to park in your demised space, then a bunch of ex-clampers putting up some signs saying that you do need a permit otherwise we are going to invoice you £100 each time that you do not display one, is not legally enforceable. So, what does your lease/AST say about parking?
Also, you should never have revealed the identity of the driver as their Notice t Keeper (NtK) is not fully compliant with all the requirements of PoFA. If the driver is unknown to them, they cannot transfer liability to the Keeper. Have you blabbed the drivers identity when you communicated with them? There is no legal obligation on the Keeper to identify the driver to an unregulated private parking company and the only way they would know the drivers identity is if the Keeper blabs, inadvertently or otherwise. When referring to the driver, do so in the third person only. No "I parked here or there", only "The driver parked here or there".
No one who is here receiving advice and following it pays a penny to the CPM.