How we worked this out (caution: contains maths and physics)

Recall from GCSE physics classes:

Q = m * c * θ

Q = quantity of heat, in Joules
m = mass, in kg.
c = specific heat capacity, in J kg^-1 K^-1
θ = temperature change

A standard cup holds about 250 ml., and of course a litre of water weighs a kilo by definition; so that gives m as 250g., or 0.25 kg.
The specific heat capacity of water is 4180 J kg^-1 K^-1.
If we start with our water at 20° and heat it to 100°, that is a temperature change of 80 Kelvin.

Filling in the figures, we get

Q = 0.25 * 4180 * 80
 = 83600 J to make one cup of tea.

One kilowatt-hour is equivalent to 3 600 000 Joules (a watt is one Joule per second; there are 1000 watts in a kilowatt, and 3600 seconds in an hour)

∴ 1 kWh is enough energy to make 3600000 / 83600
 = 43.06 cups of tea. ■