From the picture, it looks like you have a ferrule at the end of your cable. The ferrule is clamped onto the carb, but the cable housing is moving because it's not attached permanently to the ferrule.
I suggest that you remove the cable and housing altogether. Remove the cable from the housing, clean the cable and try and get the crud out of the cable housing. Grease it with lithium grease, and reinstall, but without the metal ferrule on the end of the cable i.e. clamp the cable housing directly to the carburettor.
Let us know how you get on...
'71 Series IIa "Horace"
88", RHD, 2.25 petrol.
New Zealand.