They could only successfully claim that if they actually tried to prevent cars from parking there, by notices, markings, barriers etc. And even then it would not automatically absolve them of liability.
What you should or should not do is not relevant. This situation is all about the duty of a carpark owner. There is a 'it is your own fault' defence, but where lawful visitors are concerned it is pretty much limited to you intentionally jumping in a front of a train or something like that.
Good point about the sign though. ATTAK Z you need to photo that and any other sign on that carpark. If it contains exclusion clauses it might be fatal to the claim.
I'll get a photo of the sign and post later
Thanks for all the help guys