I'm with Ford_Escort on this one. Sounds like an accelerator pump problem.
Easy to check. Assuming it's the standard Weber 32/36 carbie, remove the air filter so as to be able to look down the barrels of the carbie, and while looking down the barrels turn the accelerator linkage to open the throttle. You should see a squirt of fuel being pumped into the primary barrel out of the accelerator discharge nozzle which is located at the top of the barrels, protruding towards the center of the barrels from in between the barrels. Although there are 2 accelerator discharge nozzles, 1 per barrel, only the primary barrel should receive a squirt of fuel which if memory serves me right will be the barrel closest to the rocker cover. If no fuel is squirted into the primary barrel, then you have a problem with the accelerator pump circuit. This could be caused by a damaged accelerator diaphragm, a blockage in the accelerator pump circuit, or damaged accelerator discharge nozzle.
Good luck, and let us know how it goes.