Gravity or some times called thermo syphon is still used with some oil fired central heating units, as it allows the boiler to cool by heating the domestic hot water (DHW) some oil boilers don't have a built in run on to cool down.
There are three stages of thermo syphon, one simply switches pump and boiler on for CH + DHW and no pump just boiler for just DHW. But this system was not very good in the summer, as either the boiler would keeps cycling on/off, or you had to guess how long to run boiler, so there was the version two with a cistern thermostat, but the thermostat only does anything in the summer, then there is the third option when a motorised valve is used for the DHW which removes the whole idea of it being used to cool down boiler, but means DHW can be cooler than the CH water.
The Y Plan is a good alternative as it allows the boiler to still heat the DHW when switched off, as the valve is default with no power to DHW, however it needs more wiring, as the thermostat on the cistern needs at least three wires, nearly every other system only needs two, and the earth, and also it needs the N/C contact in the programmer or programmable thermostat to be connected, so it would require quite a bit of rewiring.
The Y Plan is likely better, but one has no option, you need a thermostat on the cistern. I did consider it for my own house, but getting three core and earth cable from the flat under main house to airing cupboard in upper floor centre of main house would be no simple task, so I abandoned the idea.
There are some wireless options, but rather expensive. So I am guessing some thing like this

has been wired i.e. all the extra wires needed for Y Plan are missing. This

would be normal Y Plan, but for the life of me I can't work out why. I would have left as C Plan, my own C Plan has extras,

so I can turn off the flat and use two pumps, and it has motorised valves so I can select main house or flat, but this is rather unusual. And there is a relay missing so can't turn off house. I can only turn off flat. Without the circuit diagram I could see anyone trying to work on the central heating becoming confused, so once one redesigns one really does need to leave a plan, as anyone following will not have a clue what has been done.