I was over in 'Non-iron' a few years ago, when gas fired heating was relatively new. Many houses used oil to heat the radiators, but an immersion heater to heat the water, it being cheaper to use electricity than to use oil. Some of these houses had an ingenious external immersion heater added beside the hot water cylinder. It is called a Willis heater, invented by a company in the Belfast area. Essentially this was a 3kW 12" electric immersion heater mounted in a copper enclosure, similar to a piece of large bore copper pipe with a 2 1/2" boss at one end (to mount the heater), a pipe tapping point to the side (near to the boss), and a second pipe tapping at the other end. Cold water from the bottom of the cylinder was piped to the boss end, and the second tapping point was oriented higher than the first to allow the heated water to rise and connect to the cylinder open vent pipe close to the top of the cylinder.
The claims were that the heated water would stratify and the cylinder would heat from the top down. The instructions indicated that, from cold, this heater would produce enough hot water for a shower in 5 minutes, and a bath in 15 minutes.
So, OP, if you're considering replacing your hot water cylinder, you may benefit from adding a Willis heater. I believe an unvented cylinder version is also available. Bear in mind that most modern cylinders are designed for pumped primaries, so may not work very well on the gravity circuit you have at present. It may be quite simple to alter your gravity pipework to incorporate a circulating pump, in which case you may get a full tank of hot water and not need to change it. You will be wise to add some safety features, such as a tank thermostat, and a 'normally open' zone valve, to prevent overheating of the hot water.
MM