SNAFUing this up! DO NOT conduct ANY communication by phone. Anything agreed or denied on the phone is not worth the paper it isn't written on!!!!! They are relying on you being low-hanging fruit on the gullible tree who is likely to pay up out of ignorance and fear!
Are you the lease/tenancy holder? If so, what EXACTLY does the lease say about parking? What it doesn't say about parking is equally important. For example, does the lease say anything about requiring a permit to park in your assigned space or car park?
What on earth do you mean by "other registered driver"? Where is this "register of drivers"? There is only a Registered Keeper and the only way anyone would know who the drover was on any one occasion is the driver themself or the Keeper. The Keeper is under no legal obligation to identify the driver to an unregulated private parking firm. So please try to understand the terminology.
There is the vehicle. The vehicle is registered (only for tax purposes) to either an individual or a company. There can be any number of drivers that can drive a vehicle. They do not have to be related to the vehicle or the Keeper in any way. For example, my own car insurance also insures me with third party cover to drive any other vehicle with the owners permission. If there a millions of people who have that type of insurance, then there could be millions of possible drivers for any particular vehicle.
All you need to know is that only the driver can be liable for the PCN, assuming it is a valid one, unless the PCN is fully compliant with ALL the requirements PoFA 2012, in which case, they could transfer liability from the driver, if unidentified, to the keeper.
Right now, you have received two Letters of Claim (LoC), One is for two PCNs and the other is for a single PCN. Are these for the same vehicle at the same location, just different dates? You are not obliged to respond to an LoC but it ay be useful, as they will be required to show what evidence they rely on to prove their allegation that the driver breached a contract with them.
Before you respond to any LoC, show us or at least tell us EXACTLY what the lease says about parking. We can then advise on how to move forwards.