For now, unless we can confirm that the you have been formally named as a party by Thorpe & Co, they have no legal standing to act. All we know so far is:
'They' (presumably their fleet/line manager) have passed their details to 'them' (assuming Thorpe & Co) and their address as they have accepted responsibility for this. "I accept I parked there for a matter of 5 to 6 mins whilst performing my duties."
The PCN (invoice) would still need to be reissued in your name. The next steps (before you receive anything) is to confirm whether Thorpe & Co has actually processed your details.
You should check with your fleet/line manager whether Thorpe & Co has acknowledged receipt of your details. Just because the fleet manager says they passed it on doesn’t mean Thorpe & Co has actually updated their records yet.
Do nothing until there’s direct contact from Thorpe & Co in your name. There is no point in acting yet if Thorpe & Co hasn’t reached out. If they don’t send anything, you don't need to chase it.
Since you are already collecting evidence of signage, you should continue without alerting Thorpe & Co.
Keep the Union in the Loop (if applicable). If you are a union member, you should inform them now before any official demand arrives. If the union gets involved early, they might help push it back onto the Council.
That’s it for now—no need to act until Thorpe & Co actually contacts you directly.
Feel free to direct your fleet/line managers to this thread or use the information in it to point out their failures in getting this PCN cancelled in the first place because it was not enforceable in the first place.