A boiler and a hot water tank ... what is this configuration? (UK)
Yes this is common in the UK.

The boiler will feed hot water into the heating coils in the tank as well as providing the hot water for the radiators.

The electric (or immersion) heater will be there either as back up (in case the boiler fails) or to heat the water on cheaper electricity (Economy 7) overnight.

There'll be a thermostat on the tank which feeds back to the boiler to turn off the heating when the water is hot enough, but other than that there's no direct communication between the immersion heater and the boiler. There might be communication via the timer used to control when each is turned on, but that's not usual.