Put heat pumps in all of them, problem solved and you cut out gas requirements exponentially, bringing us one step closer to energy independence.
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But are air to air heat pumps less efficient or something? (I read this, but don't know why, or if it's true)
Ground source heat pumps are the best, that goes without saying, but not everyone has room for them. As for air source are, they're still far far better than a combi boiler. Like 300+% more.
Retrofitting air heating/cooling into a house designed around central heating is probably difficult too though. That's probably the big issue.
I guess you would need an air con unit in every room, you could probably get the refrigerant pipes through the walls/floor?