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Strangely, all the info I've had is that the immersion is cheaper...

Check your bills. Last time I looked (UK), electricity was somewhere between three and four times the price of gas per kWh.

Your boiler can put more energy into the water in the cylinder more quickly than an immersion heater; the latter is usually 3kW while even an old back boiler could potentially output 12 or 15kW. A modern boiler can usually supply more than that, with a typical "system" boiler capable of 25 or 30kW.

Several factors in play here:

• the boiler coil may not be able to handle all the heat the boiler can supply, though even a standard coil should manage more than 3kW - the normally-quoted "recovery time" (time to re-heat the cylinder from cold) is around 30 mintues. A "fast recovery" coil will handle more, and heat quicker.
• An immersion heater (as usually installed in an otherwise gas-heated system) heats only the top 1/3rd or so of the cylinder (maybe a half), and the water underneath will remain cold, while the boiler coil is right at the bottom and heats the whole lot. Not sure if this link will work, but here's a picture.
• Your coil may be furred-up if you have hard water, or haven't maintained proper levels of inhibitor in the boiler water - how well do your radiators work?
• This is the big one: they are controlled by separate thermostats. The immersion heater has a built-in thermostat that is usually factory-set to 60C, with a safety cutout thermostat set to 80C (I think). If the water heated by the immersion is scaldingly hot it may be that the main thermostat has failed, and you are heating water to 80C on the safety 'stat.
• The boiler will be controlled (usually) by two thermostats. The first sets the temperature of the water leaving the boiler, and is usually set to around 80C, which is the temperature at which the recovery time (and a radiator's output) is calculated. There is also a thermostat strapped on to the outside of the tank (more modern tanks have these inserted into the tank). This should be set to 60C because that is considered a "safe" temperature to avoid bacterial growth and not too dangerous if you happen to hold your hands under the tap. However, strap-on thermostats are exposed and vulnerable and (depending on design) can be knocked off-temperature quite easily.

So it's possible that the cylinder thermostat controlling the boiler could be set to (say) 50C, against the 60C of the immersion. It's also possible that the flow temperature from the boiler is set low for some reason - this is unlikely, but possible. Obviously, if the boiler is set to (say) 50C, it won't be able to heat the cylinder beyond that, however high the cylinder 'stat is set, and as the cylinder approaches 50C the rate of heat transfer will slow down.

Does this help?

Point 1 - gas is about a quarter the price of electricity per kWh

Point 2 - the boiler is heating the whole cylinder, while the immersion is only heating a third or so

Point 3 - there are at least two separate controlling thermostats, and they may not be set the same

M.