Direct use fossil fuels is the main source of space heating in the UK, as in much of the cooler regions of the world, and drives a major part of the global emissions of greenhouse gases. Climate stabilisation therefore implies a systemic change in approaches to space heating, involving some combination of radical efficiency improvement and low carbon fuels. The UK has adopted a legal commitment to an 80% reduction in emissions by 2050, in spite of an old building stock and a very high penetration of natural gas as a heating fuel. The paper presents new quantified scenarios for residential energy use in the UK to 2050, incorporating both population uncertainties and different technical pathways, including continued reliance on gas, large scale electrification, increased use of biofuels and major building efficiency improvements. Scenario modelling reveals that, with minimal policy intervention, the UK will remain locked into a gas system, but there is a range of scenarios in which this is avoided. Heat pumps powered by low carbon electricity are currently UK policy makers preferred option. We show that a shift to very heavy reliance on them would raise a number of problems, notably a major increased in winter electricity demand, and therefore peak generation capacity needs. Much greater use of energy efficiency and biofuels could play a significant role in decarbonisation, still reducing gas demand by 70% to 80%, but diversifying the risks associated with a high electrification strategy.