Yes saw the Willis system so thought it would be Ulster. Never seen it used in mainland UK. The Willis system heat the tank from the top down, very clever system, so the longer it is left one the more hot water you get, but you get hot water within minutes of being switched on.
I know it has been adapted for using solar energy.
This shows the idea of the Willis system, but I live in North Wales so not dealt with this system. I really don't know how it connects with central heating.
I have a DHW thermo syphon systems, with two pumps and two motorised valves, so simply looking at the valves is not enough to work out what you have, the so called C plan has so many variations and these are all C plan
with the first there is only time to control DHW summer and winter it will reach the temperature of boiler output in fullness of time, the next allows in the summer to limit hot water temperature but no winter control so in the summer boiler only runs when required the last uses a motorised valve so hot water temperature can be controlled summer and winter, and they are all called C plan.
The the first system it runs the pump and boiler for central heating and DHW and only boiler for DHW only, and the programmer has a mechanical lock so you can't select central heating only. but the programmer and the thermostat are two independent items, with Hive they are combined, so this
is original and Hive can do the same if room thermostat is removed and terminals 4 and 5 bridged, but electricians and plumbers don't always use same diagram so with yours it may not be 4 and 5.
But this is still C Plan
now a cylinder state has been added. It only helps in the summer. And this
is also C Plan, and not started to look at how the Willis system works with it.
I would personally not touch it, it is up to landlord to repair or up grade, don't get involved.