Jeez!!!! Stop panicking and digging a bigger hole that you have already made. DO NOT, ever, contact or communicate a useless debt collector. ZZPS are powerless to actually do anything about this, irrespective of what they say in their letters.
Shred their letters and use them as master bedding. You can safely ignore everything from ZZPS or any other debt collector and we certainly don't need to know about their rubbish.
ZZPS, their sister company CGTT and any others such as DRP or DCBL have only one job and that is to persuade the low-hanging fruit on the gullible tree to pay up out of ignorance and fear! IGNORE them and never, ever, ever, enter into communication with them.
Why on earth have you redacted the location where this occurred? I assuming it was a TfL controlled station car park. We need to know whether SABA issued this as a PENALTY Notice (PN) or a Parking Charge Notice (PCN). This is critical.
It may be too late now but you should not identify the driver off the vehicle. There is no legal obligation on you, the Hirer to do so. So, have you identified the driver, inadvertently or otherwise? The driver should only ever be referred to in the third person. No "I did this to that", only "the driver did this or that".
So, have you blabbed the drivers identity? The biggest defence you have is that the Hirer cannot be liable. Only the driver is liable and they had no idea who that was unless you have blabbed it to them.
For now, please confirm whether this was issued as a PN or a PCN. Your lease company should have passed to you a copy of their PN or NtK. Show it to us if you want advice on how to handle this, especially as you have probably blown away the "golden ticket" factor that they could have never held you liable as the Hirer.
Don't try and paraphrase anything. Show us any communication, only redacting your personal details and the reference number of the PN or PCN. Leave EVRYTHING else visible. You can remove any tin-foil hat worries about them identifying you.