Before we get into the specifics of the case, do not engage with debt collectors, they have no interest in any correspondence that does not involve payment. If you receive anything that is described as a "Letter Before Claim", "Letter Before Action" or similar, that will need a response.
From what you've said, I'd be leaning heavily on your employer to intervene. The only oversight you've seemingly made is not noticing that one of the charges had not been cancelled, that it was issued seems to be down to their failure to ensure their employees were not on the receiving end of charges.
Do you have anything at all in writing about the new parking system, in particular any evidence of you being told to provide your reg to Bob so he could input it into the system, etc.? ParkingEye can be stubborn, so getting your employer to sort it will be by far the best option.
In case you do need to challenge the matter with ParkingEye, we would need to see the following as a starter to advise on the charge itself:
- A copy of the original notice
- Photos of the signage at the site setting out PE's terms and conditions
