If the sideways movement is at the pivot end of the swingarm (which from your description sounds like it might be), might it be missing the end caps that fit over each end of the pivot rod? I replaced my bushes a while ago, and as we were refitting we noticed we had sideways play, and realised that the end caps were still on the bench. deerrrr. Putting them in properly should be a tight squeeze and no sideways movement.
If the movement you've got is at the axle end of the swingarm (ie back wheel can move sideways a bit) then that would be bushes and/or worn pivot rod.
Anyway, just my thoughts.
Peter. (have sent you a PM Paul).