It sounds like your carb is running very rich (hence the starting without choke).
You could try pumping the accelerator while turning the engine over (without choke), and if it starts spluttering then keep pumping rapidly until you can build the revs up.
Also, when was your last service? and did you change the points, plugs, dizzy cap & rotor arm, as these have a bearing on the 'startability'.
Failing that it should kick into life if you bump start it. i.e. ignition on, 2nd gear, clutch in, start the car rolling (get someone to push) and let the clutch up while pumping the accelerator to 'catch' the revs.
I am a bit confused by the
my carburettor didn't have much adjustment
what exactly was meant by this? If it was mixture related, then either the adjusting nut was seized, jet was bent, or the choke assembly was sticking - all of which can be cured.
check to see that the choke is fully disengaging, by pushing the jet assembly upwards at the bottom of the carb, if it clunks upwards then that could have been your problem.
Good luck!