@Edent @DamonHD have you considered Air-to-air? I.e. air conditioners that can work in reverse? You can get minisplit systems bought and installed relatively cheaply. (Though it won't do your hot water obviously.)

@vksxypants @DamonHD yes, but the cost of retrofitting air conduits through the whole house is prohibitively expensive.

@DamonHD @vksxypants Interesting! Sadly, I think they still fall foul of my permitted woes. I'll do some more investigating.

@Edent @vksxypants The rules are continuing to unbend, though mini-splits may not benefit yet from grants or GDPOs. If you find out, please say.

(Given that I am doing a PhD on decarbonising UK home heating, I am unreasonably interested in the detail!)