Washing machine electricity
There's no reason for a washing machine to use that much electricity unless it's heating the water.  

If it's heating the water, it's using a resistive element.  With those, if voltage changes a certain percentage, power drawn changes by the square of that percentage.  So looking at the specs, it is 2000W at 220V and 2400W at 240V.  The new voltage is 109% of the old, square that and you get 119%.  The new wattage is 120% of the old.  Close enough: it is behaving like a resistive element. 

2400 watts at 240V, that is 10 amps, which is obviously under 13 amps by a margin.  You should be fine.