To get the possibility of having just the radiators on without the hot water, you would need to:
Replace the existing 2-Port valve with a 3-Port valve that can divert the hot water from the boiler to either just the radiators, just the hot water cylinder, or both together (Y-Plan)
Or add a second 2-Port valve that opens / closes the supply to the hot water cylinder, in the same way that the one for the radiators already does (S-Plan)
Both of the above systems, when wired in conjunction with a cylinder thermostat will stop water from the boiler flowing through the hot water cylinder once it is hot. When both the Heating and Hot Water are up to temperature, the boiler and pump will shut down and save energy.
At the moment, hot water from the boiler will continue to circulate through the hot water cylinder whenever the the boiler is on. When heating is also required the motorised valve will open and let water flow to the radiators, but the water will still continue to circulate around the hot water cylinder even if it is already hot, as there is nothing to stop it doing so.
You can't have only radiators 'on', because all that would do is open the motorised valve. The hot water also has to be 'on' at the same time to fire up the boiler and pump.
You can have hot water only, because the radiators are off when the motorised valve closes, and the boiler and pump continue to run supplying just the Hot Water cylinder.