Turning Off Hot Water Tank

Do you only have one timer that turns on the heating? If you had two one of them most probably turns off the water heating zone.

On your second picture, the pipework has the mechanical valve parts of two separate zone valves fitted. These valves have the actuator heads missing from their steel mounting plates. The actuators would normally be controlled by the system thermostats, time switch or programmer. One of those valves will control the flow of heated water to your radiators and the other valve will control the flow of heated water into your cylinder heating coil. As the actuators may never have been fitted or may have subsequently been removed, you still have the option of manual flow control. The centre of each valve has an operating spindle which can be rotated by 90 degrees in either one or the other direction. The spindle has a flat on the end and you may need to turn the spindle with a tool such as pliers, adjustable spanner or indeed, even a small open end spanner of a size to fit the flats of the spindle. Identify which of the zone valves has a pipe running to the side inlet of the cylinder. This will be the hot water valve. Turn the spindle by 90 degrees and that is your heating of the water in the cylinder turned off. You will still get water from your hot taps, it will just no longer be heated by the boiler.

Sounds like a good idea to change to a combi boiler