Re: and your hot water (@ David Pickles
" I'd like to be able to set the hot water according to the use I intend to make of it, and not be forced to store a tankful at a far higher temperature than I would ever need."
See other comments on legionella. A close relative has a usually benign and not uncommon condition that makes them vulnerable to respiratory infections (we all know somebody like this, who gets a cold, and "it always goes on my chest"). By turning the hot water tank down to 40C I might save around £20 a year if it is properly insulated. Is that saving worthwhile when it exposes said relative to legionella?
The reason water is stored at relatively high temperatures in the first place was of course nothing to do with legionella, and everything to do with the fact that unless you were very undemanding, instantaneous heat demand could not be met by combi boilers or electric water heaters. In the summer this is less evident, but for several weeks (sometimes months) each winter your heating system runs very close to full capacity, and there's big downsides to sizing a boiler for both worst case weather, plus maximum instantaneous how water demand.
Regarding your "could it be done" question, the answer depends on how much hot water you want and how fast. Think for starters of an instant electric shower. Tolerable in summer, when you might get 7 litres of warm water a minute out, crap in winter (as the incoming water temp is far lower) when you'd get around 3 litres a minute. If that flow rate is adequate for you then they're cheap as chips to buy and a few hundred quid to have fitted.
Most people want rather more. For illustrative purposes a decent shower is normally considered to be upwards of 10 litres a minute and most power showers will easily deliver over 20. A 7 kW elec shower takes around 30 amps. You could parallel up two of those, and you'd still have a weak 6 l/min flow in winter, but you would be at the limit of the typical domestic supply, usually designed around 100 amps (the balance being needed for other potential elec uses - kettles, TVs, hair dryers, white goods etc). So electricity can't do it unless you've got a fatter pipe coming in than is normal and a new consumer unit - all of which can be done, but it will cost a hell of a lot to do that. By the time you can get (say) 15 litres a minute in winter, you'd be pulling 150 amps just for the shower - it just makes less sense than storage.
Gas combi boilers can work, but only up to a limit - typical largest combi is 30 kW, with up to 25 litres a minute at 30C temperature lift. In practice that's big power shower territory in summer when you could get the full 25 litres a minute. But in winter 30C over 4C means you start tapping it down. Obviously whilst the shower is on the heating is not, but if its a quick shower then thats not a problem. But that's £2k before fitting, £3k when fitted (so double the cost of a normal combi) it's floor standing, so you usually lose a kitchen cupboard, and if you don't already have a combi system it will cost around £1k to modify the house plumbing. At the end of all that you've got a spent £3k on a mongo combi boiler that will be very inefficient for space heating because it is dramatically oversized (an adequately insulated mid sized detached would only need a boiler half that size for space heating).
So in short, you might get what you want, but it'd cost an arm and a leg