The camera was returned with a new top plate. Almost immediately the issue of multiple activations with one press started again. It was getting quite irritating so that I diddn't want to use the camera. Contacted Fuji and they asked me to sed it back to them. All free postage by the way.
They had it for a week but couldn't recreate the issue so nothing was done to it. It was returned and the issue seems to have gone. Let's keep our fingers crossed that it remains so.