Hi Nick
If the cable inner has broken off at the carb end then in theory you should be able to gently pull out the cable inner from inside the car. If it snags when attempting to pull then it might have a kink and I would stop at this stage as the plastic components where they attach to the plastic steering cowl are flimsy. It might be worth checking for kinks along the exposed metal inner at the carb end before attempting this. I personally would take out the whole of the inner and outer together by pressing the tabs indicated by Andy above at the cabin end and disconnecting the warning light cable too. With regards to the carb end, loosen the 8mm spanner size bolts holding the cable in place, pull out the cable inner if still attached. You can re-use the old cable outer if different to the new one, insert the new inner, check for free movement, you could also grease the new inner before fitting for smoother action. Offer up and route the whole cable, fit with the choke flap in the fully open position and make sure the cable inner is at full stretch when you do this, lock the x2 8mm spanner size bolts (avoid over-tightening especially the one which holds the cable outer in place). If you have excess cable inner at the carb end which impedes operation, you can snip it off. Avoid cutting off too much as you need some length at the carb end for future adjustment.