"Dane Koekoek" wrote
| The tank is an old copper one with a lagging jacket (no foam
| insulation here!) You can certainly feel that only the top small
| portion of the tank is actually being heated. How can I improve
| on this?

The immersion heater is only heating the water at the top of the tank
because of it's length. It might not be possible to fit a longer one, as the
coil inside may be a physical obstacle.

| I know they should heat it by the coil inside the tank as this will
| heat the whole tank, but they don't want to go down this route -
| they say it's too much hassle replacing the old boiler!

The *best* approach would probably be to replace the cylinder with a
factory-insulated one with top and bottom heaters/stats, especially if the
boiler is not to be replaced. The bottom heater can be switched on when a
bath is required, and the top heater only is used for small quantities of
hot water (washing-up etc).

An alternative would be to fit an electric boiler to the coil, on a pumped
primary loop. They're 10kW (would require new circuit from consumer unit)
and smaller than an instant shower over a bath. In some small, very well
insulated new homes, they're used for the central heating radiators.

Owain