Push the choke knob fully in and then have a check of the choke flap in the top of the carby....it should be fully open.
Next pull the choke knob fully out and see if the choke flap is in the closed position.
If so, the choke flap isn't the problem.
Sometimes the outer choke cable can dislodge from the retaining clip/clamp on the carby so check that it hasn't came out.
Do you have the older wire type outer choke cable or the plastic type outer choke cable??. The cables can seize due to lack of lube, especially the outer wire type ones......WD 40 is best to temporarily free up seized cables.
You can also adjust the choke idle speed by adjusting a screw down on the carburettor choke linkage near the throttle butterfly shaft.It runs on a cam and pulls the throttle on as you pull out the choke.
Or............ it could be something completely different............. very hard to diagnose problems without actually having ya head under the bonnet
There's a couple of things to start looking at.......
Hope that helps
I can't think what to write here so this will do.