Might be coincidental - you thought you ran out of fuel but that was maybe when it 'decided' to start playing up. That's if as you say, you now have fuel but no running.
So maybe you actually have an ignition problem - when it has cut out, try removing a spark plug and resting against engine, check for spark. If while you're doing this, there is a spark and the engine starts again, maybe Custard's right and there is a partial blockage in the tank unit. Remove from under back seat.
If there is no spark however, check crankshaft sensor connector under expansion tank or any other likely causes.
Another possibility is the fuel pump relay - maybe the fuel pump runs during starting but not while engine is running? Listen for pump under the back of the car. Fuel pump relay (near battery) is a special type, best to swap for one off another Uno Turbo.
-Alex