Mine has about 2mm of play in it. Gives a slight clunk when on the bike stand and I lift the swing arm. Can't see it move. I can feel it if I put my fingers around it.
There are five bearings that can give rise to some movement (6 if you count the swing arm bearings themselves) but if your MOT man knows about dirt bikes he should be less harsh than with a 140 mph road bike.
You have the top and bottom shock bearings, two others in the relay/linkage arm itself and the bearings that join the drop arm to the swing arm.
A little bit of movement in each can result in perceptible movement when the TTR is on the stand and you lift the wheel up and down gently.
It is very difficult to work out exactly which bearing(s) are worn. The lower shock bearing is the usual culprit but I have had occasions where I have replaced it only to have to go back and replace the others because the play was still more than was acceptable to the MOT man.
It is likely that you may still have a small amount of play even with all new bearings fitted.
Seems like the lower shock is the culprit. It's only minor I'll keep an eye on things and change when it starts to get worse. I plan to strip/replace the whole lot at some point. Just so I know I can trust them.