Your washing machine is likely an order of magnitude more efficient than you. A cycle in my machine consumes something like 0.2kWh.

From what I understand, the dryer is a bigger concern. In the UK and in Europe, you are already ahead of the curve by reducing use of the electric dryer.

A heat pump dryer is 4x as efficient as a resistive electric dryer which would reduce your operating costs by 75%.

Any of these that are electric is where your money is going: heat, water heater, air con (if you have it), clothes dryer, oven. Switch them to Russian natural gas for the savings.