When the motor's running, the vacuum is in pulses but not as deeper vacuum as what you can suck, so in operation the fuel flow is more of a trickle...If you put the vacuum hose back on, and hold the fuel hose horizontally in a bottle with the motor idling, there should be a steady approximately half flow of fuel. By that I mean it will be sort of half the hoses diameter, but trickling out steadily..

Turn the fuel tap to prime if it's a vacuum operated tap, pull the fuel pump's vacuum hose off the carby and suck hard on it, and when you let the vacuum off the fuel should come out of the fuel hose as a full diameter slug of petrol. Be cautious when you suck the hose because one possible problem is that the fuel pump's diaphragm might have a hole in it and you might get a mouthful of petrol. If the fuel delivery is a full hose diameter pump of fuel, then the pump works. You need to have the hose laying horizontally into a bottle to get a good idea if it's a full flow. If that works then you need to check there is plenty of vacuum at the carby and that it's getting to the pump. There might be a hole in the vacuum hose.