Some of you have noticed that the Enormous Heat Pump solution is not always ideal and costs a lot of electricity, especially if always on.
I did something else, starting from 2kW(peak) of solar panels often (not always, and daytime-only) having more than 0.5 kW of spare generation.
For an energy budget of "a few kWh" on "a few days per week" "daytime only", I got a small air source heat pump for one room, which really is exactly a reversible air-conditioner. That uses 0.7kW(electrical) to make up to 2.2kW(thermal). In autumn, I open the door from the living room to the stairs, activate the heat pump from 10am until 2 if sunny or less than that if less sunny, or not at all if warm enough already, and I get as much heat as possible from free rooftop solar electricity. In winter, I close the living room door to keep more of the collected heat down there.
That is a partial solution; I still use the gas combi boiler and conventional gas central heating, but not a lot; averaging 4.5 kWh/day of gas use at present. To get this to work, your starting point has to be from a house with adequate insulation.
This week, I've not always been in or the weather was not sunny, so the small heat pump has only been on for about 4 hours in the week, using gas central heating instead, on for only a few minutes and only when needed. 18 to 18.5C is my usual indoor temperature for winter except while heat pump is running, which gets 21C in the living room.
The collector for the heat pump is intentionally located in the sunniest corner of the garden, so that it is moving heat from moderate outdoor temperature to moderate indoor temperature.