Coal, mostly.
Electric boiler is almost always less efficient than a heat pump. Air source heat pumps can be an exception - some types have been known to start using trace heating to defrost the evaporator coil, with consequent COP of less than 1. An electric boiler is already over 99% efficient at converting electricity into heat, as is an old-fashioned electric fire.
Unfortunately, the national grid is only about 35% efficient at getting the energy in the coal converted to electricity at your plug socket. This is why micro-renewables are good - fewer losses in distribution.
Micro-hydro is very often impractical (you need a lot of water and a lot of vertical height, or both, to get any meaningful amount of electricity), wind works better on a large scale (make an investment in a co-operatively owned wind farm?) and solar is expensive and none of these technologies are entirely environmentally benign, though they are generally much better than buring coal. But you are right - renewables are going to be more expensive than our current (but not our future) cost of fossil fuels.
The best thing we can do at home is insulation, and lots of it, to reduce the need for heating. My late Victorian house has not been heated since half six this morning (except for heat losses from the hot water cylinder and pipework from the boiler to the coil, by the sun coming through the window, by the tiny amount of heat given off by the fridge/freezer, and (right now) by my laptop and two LED lightbulbs). Ground floor room air temperature is now between 16 and 17 degrees Celsius at present so I will probably not bother with the heating this evening.
In short, we are going to have to meet in the middle - a combination of reducing demand and finding new sources of energy. An uphill struggle though, as although we have changed fuels many times in the past, from wood to coal, and from coal and coal-gas to North Sea gas, we have always gone from a more expensive and less concentrated fuel to one that is cheaper, easier to transport, and process, and of greater calorific value. Renewables are very unlikely to allow the transition without significant changes.