THe main unit appears prety standard and contains two seperate
heater elements. Interestingly though, there is what I think is some
sort of "header" tank that sits on top of the main cylinder and
contains cold water as well as the ballcock and the overflow.

It appears that you have a combination cylinder.

If you replace it, consider installings a mains pressure system instead.
This will be much more expensive, but will provide oodles of hot water,
provided your cold taps already give excellent performance.

Unfortunately, they can be quite expensive, but if you choose a heatbank,
they are easy to fit. If the expense is too much, you may be able to fit a
pump to a conventional cylinder. These won't be quite so reliable and will
be a bit noisy, but a lot cheaper.

Christian.