You can safely ignore DCBL. They are powerless to do anything except to try and scare the low-hanging fruit on the gullible tree to pay up out of ignorance and fear. They are not a party to the contract allegedly breached by the driver. Use their letters as kindling. Ignore them.
Whilst you may have subsequently update your V5C, NGPM can only make a single request to the DVLA for the Keepers data and that would have been within a few days of the alleged contravention. So, NGPM hold an out of date address. DCBL did a simple credit reference search and found your current address and have sent you a useless debt collector letter.
You cannot leave NGPM with a choice of two addresses for you. You can guarantee that should they try to litigate, they will use the old address and you will have no idea that a claim was made until you discover a CCJ that was issued by default, later on. Your immediate concern is to send NGPM a Data Rectification Notice (DRN) to their DPO instructing them to update their records with your current address for service and to erase your old address. The highlighted words are there for a reason and you should use them in your DRN.
That will ensure that you don't fall foul of NGPM trying to get a CCJ by default. If they have the correct address for you, I can say with greater that 99% certainty that should this ever go as far as a county court claim, it would never reach a hearing and would be discontinued as long as it is defended.
However, that is a long way off, if ever happening. As it is now too late to appeal the Parking Charge Notice (PCN), the only other way to get it looked at as an appeal would be to send NGPM a formal complaint as they are required by the BPA/IPC Private Parking Single Code of Practice (PPSCoP) section 11.2 to consider any complaint as an appeal if it appears to be one.
Before that though, we need to establish whether the vehicle was permitted to be parked in the disabled bay in the first place. It is not necessary for the driver to have a blue badge, only that an occupant of the vehicle has a blue badge. Was this the case or did the driver simply ignore any signs that made it clear that it was a disabled bay for blue badge holders only? Or does the driver have a protected characteristic that is recognised under the Equality Act 2010?