The sign permits all loading, commercial or private and from/to any vehicle, so you need to submit reps based on what you have told us, and also give some detail on the nature of the goods being taken to your office.
It would speed matters up if you can give some detail about why you were undertaking this task, and also that you left the vehicle locked-up whilst you conveyed the items to your office. They will probably come back with some tosh about having to be by the vehicle whilst loading etc etc. It is part of their gaming of the system that they send out Fob-Off letters to encourage you to cough-up. You need to stand your ground and forget about any discount, just go for it and be prepared to take them to London Tribunals.