After a few years of being a bit unreliable, our boiler finally gave up entirely when we turned it back on a few days ago after the summer (the temperatures here in London started getting a bit too cool for my mother.) We've been having quotes for a new boiler, but also for replacing it with an air-source heat pump "boiler", a device which would pump heat in from outdoors, but otherwise fit into the system the same way the current gas boiler does. The technology is here, it works, it saves burning carbon, and even if the electricity is generated from gas it can actually be more efficient than burning gas on-site to heat water directly.

(In the meantime the reversible mini-split aircon we finished installing (in only the downstairs rooms) recently is also doing a good job heating the living room and uses only a few hundred watts while active, much less than a resistive heater would.)
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@pippin That's pretty neat. Which reversible mini-split did you end up installing?