If you have a 12V power supply at about 1A (or more) there is probably an existing relay that you can use with 12V instead of 220V.
Or, you can move the 220V motor connections over to a new relay with a 220V coil.
There is something wrong with your wattage calculations. 220V x 1.2A = 264 Watts.
12V x 0.8A is 10W.
Sometimes they might give the peak start-up current so the ratings/calculations may not be "perfect" but something seems wrong.
...The wattage and physical size should roughly correlate to pumping-power.