Motorised zone valve most likely.
You’ll have two x two-port valves ( a valve with a motor on top and a pipe running straight through it) or a three port valve( a t-junction in the pipework with a motor on it).
Each valve will have a manual slider to operate the valve – locate the valve that serves the hot water cylinder and move the lever till you hear a click and you should be able to lock it open. If the timer is calling for hot water when you do this, and the boiler fires up and heats the tank, then all that is needed is a new motor – ~£30 on t’internet and an easy DIY.
HTH
Edit if that doesn’t work, it might be. Dodgy cylinder stat on the hwc – a cheap component to swap yourself before calling in the professionals. Be aware that it is likely that it is 240v so if that isn’t your thing, get a professional out.