The only other components of the system that I can see are one motorised
valve (I'm not sure if that controls the water or the heating), and a
pump - presumably for the heating.

The most common arrangement when you have fully independent control is a 3
way valve to choose heating, hot water or both and a pump that pumps both
water and heating. However, you do sometimes get arrangements such as having
a gravity loop on water controlled by a zone valve, whilst having the
heating controlled by the pump.

Looking at the zone valve, does it have 3 pipes coming out of it, or 2? We
need to identify if you have S-plan (unlikely unless you've missed a zone
valve), Y-plan, C-plan or some other control arrangement.

Your modifications/repairs should include ensuring that you have either a
room thermostat or a flow switch that turns off the boiler when the flow
through the radiators drops down low.

Also ensure that you have a cylinder thermostat that does the same for the
hot water.

Christian.