Just to note that the video stops before your wife has fully left the box, but I agree that the video shows no stop at all in the whole video. So submit representations based on no stopping occurred in the box.
You'll get the usual Fob-Off letter, so if you want to stand your ground, you'll need to register an appeal at London Tribunals. Havering do not re-offer the discount when rejecting representations, so if you submit them, it is a total no-brainer to register an appeal with London Tribunals, because only the PCN penalty is at risk, there are no additional costs, and, of course, if you win, you pay nothing, but Havering will have had the PITA of preparing an evidence pack and also paying the adjudication fee.
The alternative is to cough-up now, and join the Mugged CLub.