blue is modern and well insulated.
If the immersion heater element's thermostat goes faulty, you will find that the water gets hotter and hotter if left permanently on, getting scalding hot and possibly eventually boiling. But as you have a blue cylinder the immersion heater will be quite modern and I expect it has an overheat cutout which will cut power if the thermostat fails and it overheats. If you take the plastic cap off (with the power turned off) you will probably see a manual reset button on the cutout.
This fault is rare, and usually seen on very old appliances, but the results can be very severe.
modern pipe lagging looks like
this. It is a stiff but flexible polythene foam, very durable, and can be cut and trimmed with a breadknife, and vinyl tape will hold it tight on bends. Most likely the pipe coming out of the top of your cylinder is 22mm diameter. You can get a superior "bylaw" grade that is thicker, but you may not have room in your airing cupboard. This grade is not essential indoors in heated spaces.