I checked this with Nev Metson, a retired fraud squad officer who knows more about the relevant legislation than anyone else. He wrote:

"The Achilles heel in this legislation for the private parking company is that once the registered keeper has named the driver, then the registered keeper can no longer be held liable, irrespective of whether or not the private parking company gets its money or not from the driver. So as long as the registered keeper provided the private parking company the genuine and serviceable name and address of the driver within the appropriate time frame, then they cannot be held legally liable for the alleged debt irrespective as to whether of not the parking company gets paid. For a Notice placed on a vehicle, the liability is with the driver and the driver only as there is no way of knowing (or proving) that the RK was ever aware of a Notice being placed on a vehicle. It is immaterial as to whether or not the RK can contact the driver. Where a Notice is placed on a vehicle at the time and which is not responded to, then the parking operator must serve a Notice on the keeper within 56 days of the date of the contravention in order to benefit from registered keeper liability. Three months is significantly more than the statutory 56 days and therefore they cannot hold the keeper liable, irrespective as to whether they find out who the driver was or not. To claim 'keeper liability' where none exists is a misuse and misrepresentation of DVLA data and should be reported as such to the DVLA.

Protection of Freedoms Act 2012 Sch 4 Paragraph 8 (5): "The relevant period for the purposes of sub paragraph (4) is the period of 28 days following the period of 28 days beginning with the day after that on which the notice to driver was given"".

28 days plus 28 days = 56 days. The link is legislation.gov.uk/ukpga/2012/9/schedule/4/enacted.