Thanks
the hot water cylinder should be heated by your gas boiler. It also has an electric immersion heater that can be used when the boiler is broken. Do not use the electric immersion heater at other times. Turn off the electric switch marked "water heater" and leave it off until your boiler breaks. Energy from electricity costs about four times as much as energy from gas.
At the bottom right hand side of your cylinder, held in place by a stretchy white cord, is the cylinder thermostat. This controls the temperature of the cylinder when the boiler is running. It will look rather like one of
these. You can adjust it to between 50 and 60. Plumbers will tell you that 60C sterilises the water more quickly, which is true, but the way cylinders work, the top will always be hotter than the bottom. Depending on cylinder size, you may want to adjust the setting a bit so it is hot enough to run a full bath, but not scalding. 60C is pretty hot (try a thermometer).
When the boiler is running, and your timer/programmer is set to HW on, it will heat the cylinder each time the cylinder stat, which is near the bottom, senses that the water is below target temperature. The bottom of the cylinder is where cold water enters to keep it full, so this may happen each time you fill a sink. This may result in the water at the top of the cylinder being uncomfortably hot. You can control this by setting the programmer to HW On about twice a day, for about an hour, starting half an hour before you expect tp be having baths and showers, and turning HW Off half an hour after your last bath or shower time. Depending on the size of your cylinder, and how much water you use, this may be about right. Many modern cylinders (of a different design) are very large and can supply a day's hot water after being heated once. This is economical on gas because the boiler and pipework are only heated once. You can reduce heat losses even more by lagging the hot pipes, especially around the boiler and cylinger. They will be 22mm diameter (some 28mm or 15mm). Measure before buying so you get the right size.
I can see your green cylinder, and probably the other controls, are around 20 years old, which fits with the age of your house. There may be wear in the motorised valve, which can cause the cylinder to get too hot, but try my other suggestions first. if the motorised valve (the blue box) is at fault, the large copper pipe running through it will get very hot when the radiators are on, even if HW is Off.
When the boiler is off, try using the immersion heater for a day. If the water gets scalding hot, the immersion heater thermometer is faulty, which can be very dangerous with an older design as the water may boil. The thermostat can be easily changed by a plumber or heating engineer or electrician. It is in a sealed tube so no water comes out when you change the thermostat. This thermostat can also be adjusted, but only after turning off the power.