I have come across this problem quite a few times over the years, it is a quick fix and better still very easy.
First you have to disconnect the choke wire at the carburettor

for that you will need 2 x 2BA spanners (or 4" adjustables), once this is done withdraw the choke cable from it's housing.
With a suitable spanner, undo the large nut that holds into the dash panel, withdraw that assembly from inside the engine bay, this is what you should have

What causes the cable to stick is just accumulated crud, just from being driven about etc.
I always straighten the ends of the steel (inner wire cable) by using a small hammer on a lead block, this makes it a whole lot easier when refitting, then wipe the cable with a rag soaked in petrol, wipe clean, then with a small piece of 600 wet n dry paper wipe over the full length of the wire cable, until it shines.
If you have a bench grinder with a wire wheel carefully offer the other end of the choke cable to the wheel,

make sure you don't let the wheel touch the bakelite handle, or it will dissappear quickly, clean it until it shines like this

Turn your attention now to the cable body, I used a .22cal bristle brush soaked in petrol to remove any scum,

then wiped it out using a soft rag, a quick spray with 'Inox' down in the base and allow it to run down into the outer flex, all the way through, wipe off any excess that has bled through the outer cable (yeah I know having a lube in there will also attract dirt/moisture).
If you are doing this on your own!!, you will need to remove the electrical switch box off the body as you will not be able to get the choke handle back into position, the groove in the handle lets a pin sit in that position when the choke is OFF, when you pull on the choke cable the pin rides up thus pushing the far end of the shaft upwards to make an electric circuit that will show the choke is on (eventually).
Once you have refitted the assembly, wipe some 'Inox" over the steel inner cable, and spray some on the handle itself, feed it carefully into the housing, fiddle it until it locates then slowly push it home, refit the electric switch and wires, reconnect to the carburettor, make sure the choke is in the OFF position, don't over tighten the small 2BA bolts as one screws into the alloy carburettor body, job done.
Time taken approx 1 hour working by yourself, cheers Dennis
