Question about heating water: M likes to boil the kettle to fill the basin, I run the tap. Which is cheaper?

Gas is typically much cheaper than electricity. If you use gas hot water, it would be much cheaper than heating water with electricity. Also, when boiling water on the stove, much of the heat is released into the house. If you are using energy to heat the house, that energy can offset the energy used to heat the house. If you are cooling your house, you have the waste of energy in heating the water and the extra energy used to remove that wasted heat from the house.