Equally important is what your lease doesn’t say about parking. For example, if it does not mention that you must display a permit in order to park in your demised location, then it is likely that your lease has supremacy of contract over whatever term requiring you to do so on the third party’s alleged contract says.
Get out of your mind that this is in any way a “fine”. You will not find mention of that word anywhere in the PCN or other correspondence you received. You are dealing with a speculative invoice from an unregulated private parking company for an alleged breach of contract under civil law.
It is worth responding to the LoC denying any liability or that you owe any debt. You should ask about the added £70 charge, specifically, whether the additional £70 represents what is dressed up as a 'Debt Recovery' fee, and if so, is this nett or inclusive of VAT? If the latter, would they kindly explain why you are being asked to pay the operator’s VAT?
With regard to the principal alleged PCN sum, you should ask whether this is damages, or will it be pleaded as consideration for parking?
Under the PAP, you are entitled to answers to specific questions, such as those above.