The thing you're describing is called an instantaneous water heater, and they come in endless shapes and sizes, tanked and tankless.
(tankless ones use no power when the tap isn't running, but need a high amp electricity connection if you want more than a warm dribble)
I think our electric shower is rated at 8kW. Makes you realise how much power it takes to heat water to a decent temperature very fast.
Would solar collectors/thermal be a plausible solution @t.o.?
@ffm started
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The thing you're describing is called an instantaneous water heater, and they come in endless shapes and sizes, tanked and tankless.
(tankless ones use no power when the tap isn't running, but need a high amp electricity connection if you want more than a warm dribble)