I don't see how water consumption is supposed to be a "britishism"
UK has a sea climate. Lot of moisture in the air and lots of rain days (50% or so).
Keeping your garden green, your grass, does not need that much water.
And UK has a culture for gardening and gardens with grass.
Much more than many other European countries. And needing more water than the nice flowers in pottery pots "gardens" in drier areas of Europe.
So, considering that sprinkling water for gardens is such a high amount in Australia, New Zealand, etc. My guess was that in the former colonies the tradition of nice grassfields for cricket, golf, rugby etc and the tradition for nice green sprinkled gardens was kept up, and became part of the traditions of those countries.