Is air-con just that rare? A heat-pump isn’t all that much complicated than a ducted air-con. Here in the US, most HVAC service companies can/will service all types (pure AC, heat pumps, various furnaces, etc).
Which is why heat waves/domes can be so lethal in Europe: people/infrastructure are not prepared for them.
* https://climate.copernicus.eu/heatwaves-brief-introduction
Same problem in Vancouver, Canada: it's a Marine climate, so when heat hits, folks aren't prepared for it.
How are most homes in England heated? Gas furnace + radiators?