Something seems to have gotten confused because a serious fault for mirror checks for a change of direction isn’t really much to do with the trailer. This is something that would be the same for a car test. Simply follow mirror, signal, manoeuvre.
It is simply the case that you made a change of direction (significant) without doing a mirror check. This could have been on the approach to a roundabout or as you change lane for the exit. It could have been on the approach to a turn where you are moving lane.
Even if you aren’t moving lane, but you do plan on turning ahead, you need to do a mirror check before signalling. You never know when a motorcycle could be filtering down your outside. You need to know about that motorcyclist.
If you are indicating for any reason you need to be checking your mirrors and keeping the all-round observation going all the time with regular mirror checks anyway.
As regards the pedestrian, you need to be aware of the hazard and proceed with caution, which may involve slowing down and/or indicating and moving out. The pedestrian could make an unexpected move at the last minute. If the other side of the road is empty and you can see far enough ahead, you are better being out and away from the pedestrian.