I live around the corner from Langdale Road.
FYI Greenwich issue visitor's permits online, on the same website as you got your residents permit. [Although in this instance loading is an exempt activity]
The letter from your flatmate is a bit weak and too verbose to my mind. It simply needed to confirm he was assisting you load heavy or unwieldly furniture and, importantly, specifying the date and time. These details are missing.
Also there is no such road as Ashburnham Road. There is an Ashburnham Grove & Ashburnham Place. Neither are realistic alternatives to the place parked, due to distance and as both would have been subject to the same parking restrictions. So why mention it at all?
However, usefully, there IS free parking on Greenwich South St. in front of St Mark's Church on Sunday. [Keep that quiet!]
The next challenge & appeal needs to be done by the Keeper not OP.
Include in the formal challenge/appeal that there was no benefit in parking illegally given the availability of free parking nearby; adding weight to the defence that you were parked in contravention only whilst - and because of - loading. Which took no more than 15-20 minutes.
Others may disagree, but I would get another version of the supporting letter, with date and time. Keeping the details of the furniture and flights of stairs.
Ask for the CEO's notes, to put the 10 minute observation to the test.
I note, from address of rejection, that Greenwich have out-sourced parking to Northampton. No doubt to to a PCN churning facility, so expect to have to take this to the tribunal.
I would suggest that this is a probable win at Tribunal, as it is a he said/she said situation, and you have evidence of moving.
But await other advice.