Thanks for the clarifications, Alistair. It seems, then, that the rich mixture problem is not due to foul play, but is a genuine malfunction. Does the smoke happen at all speeds, and is it continuous if you run the mower at full speed under a fair amount of load, e.g. if you hold it back as it mows? And is it always black, with the characteristic smell of half-burned petrol (like when you leave the choke on)? If it does, I can't think of any way for excess fuel to get through the carburetor except through the main jet. The fuel pump on the side of the carburetor just pumps fuel steadily into a small well in the top of the fuel tank. The well overflows continuously back into the tank. Thus, no fuel pump malfunction I can think of could cause this problem. (This is quite different from the situation with the older vertical crankshaft carburetors, by the way.)

Let's see if bigted or one of the members can come up with an alternative explanation. If not, it may be necessary to remove the carburetor and inspect its main jet, in case it has fallen out or has some similar problem.