A 13amp circuit is only capable of running a 2kw appliance.
1) In UK, a 13A circuit is practically unknown
2) A 13A plug, or FCU, can supply 3kW. That's why the figure was selected. At the time it was introduced, the biggest load any house was expected to have was a 3-bar electric fire, using 3kW, and the plug and socket were designed to supply it; but can also be fused down for lighter loads.
A 3kW instant hand-wash water heater is available, but the flow and temperature are about the same as a cat peeing on your hands, so they are almost entirely useless.