Heat pumps are very common in north America and parts of the Orient.
They are comparable in price to a Split air conditioner with a gas furnace - not a heating only system.
When your daily summer temperatures are >35C for 4 months straight, you need air conditioning.
A new boiler system (complete) is probably comparable to a heat pump, at least on a larger house. However, retrofitting is much harder.
Heat pumps are around 260% efficiency as a rule of thumb. Boilers are mostly 95% if you get a nice one. Below are some calculations:
34p (electric price) divided by 2.6 (COP of heat pump) means that for heating your house by 1 Kw will cost 13.4p for electric.
10.3p (gas price) divided by .95 (boiler efficiency) means that for heating your house by 1 Kw will cost 10.8p for gas.
The advantage is having A/C so you can weather the hot months (at the cost of more electric) if you want.
In the UK, you use hot water radiators? That will come with a pump energy penalty, but comparable to the fan on a heat pump or furnace.
The thing is, many appliances that use heating use straight resistance heat - which costs 34p to heat by 1 Kw - for example a stove, oven, clothes dryer, erc. Changing these our for gas versions will reduce energy use by 70%.
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