Delving into the issue of how to avoid wasting cold water while waiting for the hot to arrive, I found there are small "Point of use" indoor electric water heaters. There are
tankless models and ones with tanks. The tank less models are rated by their flow (in litres or gallons per minute) and the ones with tanks by the tank capacity.
The tank less ("instant") units have the advantage that they can heat water continuously, but require more power to do this than is available from a normal power point (they have to be specially wired). The units with tanks can be plugged into a normal power point, but only supply a limited about of water.
The units are designed to be used on their own, or placed at the end of a long line from a larger hot water system. For this purpose the smallest units (2 gallons, or about 8 Litres) would seem suitable. In my case the point of use hot water system would supply the first 4 Litres of hot water, at which point hot water would arrive from the main system and the unit's thermostat would cut out. The unit would not need to heat the remaining water arriving and would have its supply of hot water replenished. But it would use power keeping the 8 Litres of water hot, when the tap was not used for extended periods.
US Model point of use water heaters:
ps: Some bloggers have suggested turning the thermostat down or hot water system off when not needed to save power. It should be noted that authorities in Australia require a minimum temperature of 60°C to inhibit the growth of legionella bacteria. Also some of the POU heaters are designed for use with one tap and cannot be plumbed to several, nor connected to a shower.