Heat pumps extract heat from ground, water or air to heat a house. If electricity, which drives the heat pump, was generated from renewable resource such as hydro-electric dams then this will be an excellent source of heating a home.
In the UK most electricity (about 85%) is generated from fossil fuel - gas, oil, and coal. Converting the fuel to electricity is very costly in monetarily and in carbon pollution to the atmosphere. A maximum efficiency of about 30% is achieved when burning the fuel in a turbine. The rest of the fuel energy is wasted as heat into the atmosphere. The processing and distribution of this electricity wastes approximately another 20% of the remaining energy. That is why electricity cost is about 7 to 12 p per kW. Check your electricity bill. The cost of oil or gas is about 3p per kW.

COP
A heat pump will extract about twice as much energy from the ground as put in it. This depends on the area of the ground around the property. A lake or a river nearby replenishing the heat extracted would be desirable. Such pump will have a COP (Coefficient of Performance) of about 3. This way the heat pump will recover some of the energy wasted in the process of generating electricity. Heat pumps are at their highest efficiency when used with low temperature heating system. Warm water underfloor heating.
Looking at the diagram below we can see that the heat pump made up for the energy lost in generating electricity by adding free energy from the ground. So we now have 67 kW for heat out of the 100 kW we put originally in the system. This is no better than the efficiency of an ordinary gas or oil boiler at 70 to 75%. Even if the heat pump was to operate at a COP of 4 in ideal conditions then the energy extracted plus the energy put in is about 92 kW compared to the original 100 kW put in. A high efficiency condensing gas boiler has an efficiency of over 90% and a fraction of the capital cost of a heat pump.

Conclusions
From the above analyses we can draw the following conclusions:
1- Heat pumps are efficient and save energy in countries with cheap hydro-electricity. Such as Sweden and Montana in the USA. That is where most heat pumps are manufactured.
2- The price of electricity will rise as the price of oil and gas rise.
3- Burning the fuel at the point of use, in an efficient boiler, (on the premises) is the most efficient and cost effective solution.
4- The extra capital cost incurred with heat pumps can be used for even better insulation, precise temperature control and solar panels.
5- Electricity is an expensive fuel and should be used for lighting, electronic equipment and mechanical power. Such as freezers, refrigerators, air conditions and computers. It should be used for heating as a very last resort.

If you have experience in running costs of a heat pump in your home we would like to hear from you.