Sorry
@JohnW2 don't want to muddy the waters on this thread, but yes it uses convection. The problem is can't get cables from the location of cistern to boiler to work a hard wired thermostat, and the type of boiler relies on being able to cool on switch off with the thermo syphon so any thermostatic control only works in summer anyway, so I use time only to control DHW and it is in the main good enough.
My immersion heated does of course have a built in thermostat, should electric drop in price.
The Willis system used in Ireland however time is rather important, the cylinder heats from the top down, so longer it is running the more hot water, not seen the system used on main land UK, but that does not mean it does not exist. One could of course use multi-tank thermostats at different distances down, but normally uses simple time.
We are again jumping to conclusions, it may well have off peak power, but as far as I can tell
@matlob has not said that, also he has not said one timer works all, he may have four of them, or if it uses a relay of some type.
Fact he has storage heaters does point to off peak power, but next time I am at the flat, seems to point to being a landlord or uses flat on a intermittent basis. These can all change what we would consider best option, I like I am sure many others tend to look at my own situation, my flat has no time set for the heating, it heats up reasonably fast, and when I want to use it I turn up heating, otherwise it is set to a defrost setting. The same boiler does main house, and it seems the flat can starve rest of house of heat, so heats up flat first and full 19 kW into flat heats it fast.
So for me no need for timers in flat, but if using off peak power, then timers are clearly required, and they also need to be reasonably accurate and reliable. Likely connected to some form of telemetry to ensure it only turns on during off peak?
However there was a time when with off peak you paid either more for peak power, or higher standing charge, and many who were out all day realised they were better off only heating when required, I simply can't see the point in guessing.
My time switches in the main are wifi connected in some way, so as a result auto change from correct time (UTC) to daylight saving time.