Parking charge paid by Car Rental Company

I have still not received Particulars of Claim from GB Vehicle Hire, so I thought I will write my defence proposal. Could someone have a look it and tell me if the format and wording are correct:

I am disputing this claim because throughout the lease of the car, from GB Vehicle Hire, I had never received any parking fines. Furthermore, in the Terms & Conditions of the Vehicle Hire document which I had signed for the time of lease, there was nothing stated that GB Vehicle Hire could pay any fines or fees on my behalf, and then demand the reimbursement from me.
The document that ‘GB Vehicle Hire’ is referring to, is an invoice issued by a private parking company, which cannot be paid by GB Vehicle Hire on my behalf as this is not covered in their Terms and Conditions.
If GB Vehicle Hire were in doubt to what should be done with the document, then they should have discharged the liability, and named me as a driver in accordance with paragraph 13/14 of the POFA Schedule 4, so that I could have dealt with it.
By not doing so GB Vehicle Hire denied me the right to appeal and defend myself.
Events in chronological order:
On the 23/10/2017 I received the first letter from ZZPS stating that I parked the car in unauthorised way on Summer Row Car Park Birmingham University, Birmingham – Summer Row Carpark


(Source: Google Maps])

If you look at the above Google Map you can clearly see that there is no car park at this location, and there is no ‘Birmingham University’, but ‘University College Birmingham’. Summer Row Road is a public road and is part of Birmingham Council, therefore any parking tickets should be issued by Birmingham Council not by private parking firm.
The parking event as described in the letter from ZZPS (a debt collecting firm working on behalf of Elite Management Midlands LTD) dated 23/10/17, allegedly occurred on 03/04/2017 at 15:15. I had been taking notes of where I was working throughout the time of the car lease, and I did not note or recall this. On that day I worked at different location of Birmingham. I confirmed it with my boss by checking submitted timesheets.
GB Vehicle Hire neglected their responsibility to name me as the driver when they received the first letter from the private parking company (assume Elite Management Midlands). They had waited for more than 6 months to name me as driver, denying me time to dispute or resolve this issue in shorter time. Also GB Vehicle Hire did not comply with the process set out by BVRLA and in the BPA/BVRLA Memorandum of Understating, signed in 2013, following the change in the law within the Protection of Freedoms Act 2012 (the POFA)
On the 02/11/17 I received a letter from GB Vehicle Hire stating that GB Vehicle paid ‘so called’ fine on my behalf. This is actually an invoice (not a fine) from the private parking company, and they gave me 14 days to reimburse them. Also the letter mislead me by stating: “If it goes to Court then you will have a CCJ placed against you and your address which as you may or may not know will make it extremely difficult for you to obtain credit in the future”.
I replied to this letter on 12/11/17 questioning their rights to pay this invoice on my behalf, asking why liability was not discharged by them and why I was not named as the driver. In their reply from 17/11/17 I was sent a Hire Agreement with Terms & Conditions which, as previously stated, does not give GB Vehicle Hire the rights to pay any invoices on my behalf and then demand money from me. This letter falsely states that I had not received any correspondence from the issuer of the PCN, and had no time to appeal.
In my letter dated 12/11/2017 I questioned why I was made aware of this alleged PCN so late (first letter was sent to me on 23/10/17, despite the alleged parking event occurred on3/4/2017.
The second letter I received was from GB Vehicle Hire dated 02/11/17 and stated that the ‘so called’ fine, was paid for by them. There was only 11 days between the time I was notified of this alleged PCN invoice 23/10/17.
GB Vehicle Hire gave me no time to dispute it.
When I received the letter dated 02/11/2017 from GB Vehicle Hire I sent my friend to their office to clarify this issue, but was told I had to pay them the money back. This was on 06/11/17. On that day my friend received this letter in person at GB Vehicle Hire’s office which was dated 02/08/17, and was sent to GB Vehicle Hire from the PCN Admin Centre.
My friend asked the office clerk to write on the letter “received on 6/11/17” and sign this document to prove that this document was given to him on that day. (Document attached)
I have never been presented with any evidence of my unauthorised parking until present. So I asked my friend to contact Elite Management Midlands LTD on my behalf. He called them on 06/11/17 quoted their Parking Charge Notice Number: xxxxx. They stated: that this case is too old and referred him to ZZPS to clarify it. When he called ZZPS, he was told that person who got the letter needs to speak to ZZPS.

I phoned them afterwards on 08/11/17 & 09/11/17 and provided them with my e-mail address, and asked them to send me evidence of my unauthorised parking. Until today I have not received anything and any evidence from anyone. Furthermore, during the lease time I had never found any PCN attached to my windscreen.
I received a letter from ZZPS dated 06/11/17, four days after GB Vehicle Hire paid their invoice on my behalf ,demanding money from me, lesser amount this time £100 for Parking Charge and £72 Administration Fee, not £233 as was demanded in the letter from GB Vehicle Hire. This invoice was sent to me from ZZPS despite GB Vehicle Hire unlawfully paid this invoice on my behalf on the 02/11/17.
I strongly believe that I don’t need to reimburse any money to GB Vehicle Hire as they had no rights to pay any invoices on my behalf. I have never been presented with any evidence of any wrongdoing. On the specific day I was at the different location of Birmingham. There is no private carpark on Summer Row Road in Birmingham. There is no Birmingham University at the same location.
Please take into consideration above arguments and deny my responsibilities towards GB Vehicle Hire.
(I am providing copies of all documents which I received by post until now, and copy of my letter sent to GB Vehicle Hire on 12/11/17)

Last week I have copied what was stated on Claim Form under section Defendant. I am not a solicitor and dealing with this matter for the first time.
In this section is stated "I will provide the defendant with separate detailed particulars within 14 days after of the claim form."
I have not received anything since Claim Form was sent to me and as stated before I still have not received any prove of my unauthorised parking.