Yes, I wondered about a crack in the fuel feed line just under the top plate of the pump/pickup assembly. Sideways "sloshing" is allowing air in or fuel pressure to be lost (if it has a lift pump).
Do you leave a cloud of black smoke behind just on roundabouts and corners? On my ancient Passat with a well-worn diesel many years ago, blown-back engine oil collected in the air filter housing, and then sometimes on bends sloshed into the air intake, giving the engine extra nasty fuel! Damn thing would take off like a scalded cat for 50 yards or so leaving above-mentioned cloud. I hope for your sake it ain't that!
How about engine mountings slack and allowing the fuel pump cable to be pulled giving a foot on the pedal effect ?
Quick and easy check, cheap / free too !