An electric shower probably wont work at all on 110 volts. The reduced voltage probably wont operate the solenoid valve that controls the water supply.

An electric immersion heater can be used on a reduced voltage, but this is better achieved via an electronic controller than via a transformer. Consider the cost of the transformer and the losses therein.

I would simply retain the electric shower and accept that use of this appliance means importing a little grid electricity.

It sure does sound complicated. However, I do take issue with the idea that the electric shower uses “a little” grid electricity: In my household I think the shower is about ⅓ of our electricity consumption.

But isn't there a simpler form of the suggestion? Use thermal solar to heat said cylinder, and plumb cylinder output to input of standard electric shower. If the stored water is reasonably warm you can turn the power control of the shower to its middle setting, and use significantly less power. 

There may be installation instructions or regulations telling you not to connect an electric shower to hot supply, but that applies in the 110V variation as well.

As a complete aside, can I ask if:

a) With UK style 230V radial circuit, connected to a 110V transformer, if there is human type connection to either 110V wire, will the 230V circuit RCD trip? 

b) If so, what happens when the 230V side is cut off, does the collapsing magnetic field or whatever leave a potentially hazardous amount of energy still able to do damage on the 110V side? 

Gideon: 
 

As a complete aside, can I ask if:

a) With UK style 230V radial circuit, connected to a 110V transformer, if there is human type connection to either 110V wire, will the 230V circuit RCD trip? 

If the transformer has at least simple separation and there is no connection (other than protective earth) between secondary and primary, no the primary RCD cannot trip and RCD protection (if required) should be provided on the secondary. I say “if required” because in the building site Reduced Low Voltage System, an RCD is not always necessary to comply with BS 7671, but there is no problem providing one.

If the transformer is an auto-transformer, then the primary RCD is able to trip.

b) If so, what happens when the 230V side is cut off, does the collapsing magnetic field or whatever leave a potentially hazardous amount of energy still able to do damage on the 110V side? 

Stored energy would be possible, but I don't think it's ever been taken into consideration when overcurrent devices provided automatic disconnection, for example … 

The stored magnetic energy (I2 L where L is the inductance of the primary when the secondary is unloaded) may be released as a short duration transient, but the sizing of transformer cores and winding resistances is such that this transient is all over in a few 50ths of a second, or the transformer is seriously oversized… Usually enough to make a rather scary ‘pock’ at the switches, and maybe burn the contacts a  bit. This is the ‘back EMF’ spike that you may have been bitten by.

There is no exact magnetic analogy of the stored electric charge , where a charge may persist across an open circuit capacitor  almost for ever.

The nearest you get to magnetic energy storage that is the superconducting magnet, where a coil of superconducting alloy wire cooled to zero resistance has a current set flowing, and then the ends joined together. That gives a more or less permanent electro-magnet, but unless you make medical scanners or work at CERN it is not the sort of thing you see very often. The biggest risk there is not shock, but being struck or trapped by magnetic objects. (or being killed by a leak from the cooling system) 

However, like shorting the capacitor, if the superconducting wire warms back to normal, you get your magnetic energy back, as a lot of heat in a small space, and that can be impressive.

Again, not in the more normal transformer  sort of case luckily.

Mike.