Around 20% of the nation’s carbon emissions are generated by domestic heating. Analysis of the many ways the energy system might be adapted to meet carbon targets shows that the elimination of emissions from buildings is more cost effective than deeper cuts in other energy sectors such as transport. This effectively means that alternatives need to be found for domestic natural gas heating systems. Enhanced construction standards are ensuring that new buildings are increasingly energy efficient, but the legacy building stock, of around 26 million homes, has relatively poor thermal performance and over 90% are expected to still be in use in 2050. Even if building replacement was seen as desirable, the cost is unaffordable, and the carbon emissions associated with the construction would be considerable.