Its most likely that the rubber mounting between the carb and the inlet manifold is knackered letting too much air in after the carb. Very common failure in these, also check the short vac pipe off the end of the inlet manifold on its underside where you can't see, it often perishes and lets air in where its not supposed to. Get someone to press down hard on the top of the carb while you try to start the car, it probably will, and then release the pressure and it will probably stop again.
