We have a thermostat in the hallway. These photos are from the inventory before we moved in, the heating and hot water are constantly on (red light lit up) on the programmer
You can download the instructions for the timer.
They are easy enough to set.
To save gas/ electricity:
Read the timer manual and set the heating to suit. The longer it's on, the more it costs.
Turn off rooms you don't use (set the trv to 0).
Set the thermostat to as low as you can accept. Even 1c can make a big impact.
Don't use heating at night. People sleep better in a slightly colder room (18c).
One very cheap way is to not have the heating come on by timer at all, but to just use the 1hr boost when you need it.
Another way is to set the ch heating to be on all the time, but use the thermostat as an on -off switch.
Hot water does not need to be kept hot when not in use. Others may argue for convenience that keeping it hot 24-7 is best but for absolute savings, just have it on for an hour in the morning and at the evening. (To suit). The immersion should be only used for a boost (ie you want a bath and the hw is cold).
However, you have a hw boost on the boiler so there should be no need to ever use the immersion unless you are in a rush.
Your system looks basic but in good nick so should be working fine. However, if it isn't working properly, it will be a good idea to get it serviced.
With heating, be aware of hysteresis.
Things take time to heat up and cool down. If you do use the timer, allow 1/2 hr for the start-end cycle. No need to keep the gas burning if you are on your way out.
Don't turn off the heating permanently. It does the house good to not be freezing cold. If you do turn off rooms, warm them up occasionally to stop damp etc.
Hope your bills come down.l