By parking on the private land you have accepted the terms and conditions.
“When you enter a car park, you are entering a legally binding contract and by parking there, you are agreeing to abide by the terms and conditions. If a motorist has breached those terms, by say staying beyond their purchased time, a parking operator will have reasonable cause to request the registered keeper details of the vehicle from the DVLA and issue a PCN. Contrary to Penalty Charge Notices issued by a council, PCNs are not issued under statutory authority and should not be considered a ‘fine’. They are instead issued due to a breach of contract and are enforceable under contract law, potentially leading to County Court proceedings if they remain unpaid.”