I am an electrician not a heating engineer, but I think the back plate on that controller is common to a number of makes, it looks the same as the one on my Drayton Wiser, and also Hive. I looked at the Wiser instructions and like EPH it does not seem to have an option to work with gravity DHW systems, however the Hive does, it has a software option so the two relays can be arranged one to run pump, and one to run boiler, which in theroy will allow DHW without the central heating running, although not the other way around, there is no way to turn off DHW when central heating is running.
I used Nest Gen 3

because one has access to the com terminal it can be wired to only run the pump when CH is required, and the option of a ½ hour slot in the summer, allowed me to run the central heating boiler without pump 4 times a week, it would run for around 20 minutes each time, however when I had solar panels fitted, I also had an iboost+ fitted, to heat DHW with the solar power, and it tells me how much saved, which is basic how much energy is being used to heat the DHW.
This was a lot lower than expected, around 2.5 kWh per week, OK only heats top of cylinder, so no good for a bath, but oil was using around 25 kWh per week, as it has to also heat the boiler and all the pipe work, so in summer it would have been cheaper to use the immersion heater to using oil.
Also I found even with the pump not running, the radiators did get slightly warm, so I fitted motorised valves to stop the water going through the CH, but was advised not to fit them to the DHW as the boiler uses the DHW to cool down, how true that is I don't know, but that's what my oil guy told me, so I did as he said. I have no way to turn off DHW heating from the boiler, so today I never run the boiler for DHW only, but it does heat DHW when central heating is running.
So if I was starting today with the knowledge I now have, I would not even try to get boiler to heat DHW on its own, if I wanted DHW only I would use an immersion heater, it is cheaper that way, I still have Nest Gen 3 so can set it to just heat DHW, but I don't, I now use a single channel Wiser thermostat to run the central heating, in parallel with the Nest as Nest is in the hall, and the hall cools slower than the living room, and Nest will not connect to TRV heads, Wiser however will, so idea is to slowly replace the stand alone programmable TRV heads of linked programmable TRV heads at least in key rooms.
So with what I know now, I would say simply use an immersion heater in summer, and leave CH as it is.