Hot water cylinder immersion?

External immmersion in its own housing, connected in a thermal-syphoning loop from the top of the tank to the bottom.

What you now have is the normal configuration in a normal cylinder. So it should work a lot better than that. Have you checked the setting of the stat? (Should be say 80 degrees) If it is 80 degree ish I think your stat must be faulty. It's quite unusual for them to fail. Check out by connecting the immersion heater without the stat, (unless you have another stat to hand).

DO NOT RUN UNSUPERVISED, KEEP A CLOSE EYE ON IT. A couple of hours should see plenty of hot water.

External stat placed lower down? Note that normal boiler control ones won't have the rating to switch a heater, so you might need a relay. In this case you would *definitely* be safer to have an over-temperature thermostat (or "policeman") at the top.

There was a case a few years back where a faulty system was overflowing hot water into the plastic header tank. When this got hot enough it ruptured and dumped a tankfull of very hot water through the ceiling on to a small child in bed, and they did not survive.

Some tanks used to have a side entry point for an immersion at the bottom. You also used to be able to get "fit your own" boss kits which were fitted from outside. Whether you would want to do this with modern gauge tanks, even if you could find one, is another matter.

If its working properly, the long immersion and its supplied stat ought to heat most of the tank.

You could cut a hole in the side lower down and fit a shorter immersion (although you would need to dodge the indirect coil).