There's a rubber pipe inside
the fuel pump that carries fuel from the bottom "bucket" part of the pump up to the outlet tube (the one with the red/white plastic end-fittings that carry fuel to the fuel filter and then the injector rail).
The rubber pipe can split and so your petrol doesn't get pushed up to the top of teh pump... instead it leaks out and falls back into the petrol tank. The car can't accelerate as the more revs it has, the higher the fuel pressure and that means more petrol leaks out of the split in the rubber pipe.
If you lift the pump out as far as you can, you might be able to see whether the rubber pipe is split or not. It looks like normal injector hose (but it isn't "normal").
To replace the pipe you have to remove the pump from the tank.. but before you unscrew it, you first need to remove the fuel level sender tube (the smaller part, inside the fuel pump) since that goes in at an angle and the pump will not come out with the sender attached.
If you replace the rubber pipe, you *must* use rubber hose that's designed to be submerged in petrol (called "in-tank injector hose" or similar). Normal rubber injector hose will perish if you put it in petrol - only the inner lining
of a normal pipe is petrol resistant and the problem will happen again after a few days.
New pumps have a plastic hose instead of rubber... so sounds like it's a common problem.
The biggest problem is removing the fuel level sender since it will be hard and brittle and you might damage the top fittings (you have to use a special key or drift it with a screwdriver). Also the rubber gasket around the fuel pump will "stretch" (because of chemical reaction with petrol) when you take it out and it's difficult to refit it back in the hole. If you can find a new gasket before you take the pump out, it'll help you to re-seal the pump retaining ring.
If you can't find an Alfa 155 pump.. (if you need a new pump) also have a look at Fiat Tempra, Tipo or Lancia Dedra. I have a Fiat Tempra pump in my car (same part, different box).
If the rubber tube isn't split, then the problem could be a blocked fuel filter (under the right hand side, where the passenger seat is).