This is called judder and it's caused by the speed of the movement of details in the frame. Anyone that's shot film with a 35mm cine camera and has not paid attention to the critical panning speed charts has seen shots spoiled by the incorrect speed. You could try CC Force Motion Blur to hide the problems.
I would guess that the camera was set to 24P. Speeding up the shot may help, slowing it down may help, but there is no magic fix that is a one click solution. This will take some experimentation and rendering and testing playback on the target playback device at full resolution.
Thanks very much for the info Rick and yes it was shot at 24P.
Do you think AE could do a near-perfect job of rectifying the problems or would a re-shoot be the only way? I would like to avoid re-shooting if possible as it would be expensive and time-consuming.
Thanks very much for the info. Do you have any tips for CC Motion Blur settings?
I can't quite work out if the "render-only" version of Twixtor is sufficient (apologies but I am quite inexperienced with AE).