You can still use gravity or siphonage to fill up with a hose down stairs. Assuming the water butt is sitting on the floor at carpet height and your flat is on one level its easy. If you have a tap then it will work or if not drop the hose into the barrel and roll it down the stairs and suck hard. once you get the water over the top of the barrel it will carry on. Either way would be improved further by sitting the tank up on blocks.
i may have missed something but would that work? Seems the same as over the balcony. You shouldn't need a pump.
Andy