How high should I set the thermostat on my water cylinder?

For a typical domestic hot-water cylinder, the thermostat should generally be set to around 60°C.

This is a good balance between having sufficiently hot water and avoiding unnecessary energy use. For stored hot water, maintaining the cylinder at about 60°C is also important for controlling the growth of bacteria such as Legionella.

A few points are worth knowing:

50°C or below: generally too low for a stored hot-water cylinder because of the increased risk of bacterial growth.
Around 60°C: the usual recommended setting for stored domestic hot water.
Above 60°C: gives hotter water but increases energy consumption and the risk of scalding.
Much higher settings: usually provide little benefit and can increase limescale formation and energy losses.

If you have an unvented cylinder, don't simply turn the thermostat up because the water isn't getting hot enough. If it's correctly set at around 60°C but the water remains tepid, there may be a faulty thermostat, immersion heater, motorised valve or another system fault.

Also, don't confuse the thermostat setting with the temperature at the tap. Unvented cylinders can store water at around 60°C or higher, so thermostatic mixing valves are often used to reduce the temperature delivered to showers and taps and prevent scalding.

See:
https://easyflow.co.uk/articles/whats-the-best-temperature-to-set-your-unvented-cylinder