The fact is you were loading. This exemption covers all the activities related to the loading, in your case, having to bring your belongings down to the car, secure them in the car, then go back for another load. Clearly you couldn't leave the car unattended without locking it up, whilst you returned for more of your belongings.
Can you please post your reps and their response, which is normally a Fob-Off type of letter. We need to see it.
What you submitted is called an "informal challenge". To take matters further, i.e. stand your ground, you must now wait for the Notice to Owner. Are you the keeper of the vehicles with your name and up-to-date address on your V5 ?