My machine is vibrating whilst I am printing. Has anyone else had this problem? If so how did you tackle it? I am tempted to install some sort of rubber washer between the thumb screws and the plate.

A certain level of vibration is normal.
It is difficult to determine if it is excessive in your case. It all depends on print speed, object, the way it is sliced, settings, etc…
You are in the best position to judge if it is normal or not.

Are you sure its not happening when filling small spaces in the object?
Maybe you could provide a video(Youtube,vimeo)?

I also have strong vibrations after upgrading to GT2 belts. My e3d hotend is shaking, which probably causes wavy print surface