Climate change means the UK will experience warmer winters and hotter summers in the future. Concurrent energy efficiency improvements to housing may modify indoor exposures to heat or cold, while population aging may increase susceptibility to temperature-related mortality. We estimate heat and cold mortality and energy consumption in London for typical (non-extreme) future climates, given projected changes in population and housing. Building physics models are used to simulate summertime and wintertime indoor temperatures and space heating energy consumption of London dwellings for 'baseline' (2005-2014) and future (2030s, 2050s) periods using data from the English Housing Survey, historical weather data, and projected future weather data with temperatures representative of 'typical' years. Linking to population projections, we calculate future heat and cold attributable mortality and energy consumption with demolition, construction, and alternative scenarios of energy efficiency retrofit. At current retrofit rates, around 168-174 annual cold-related deaths per million population would typically be avoided by the 2050s, or 261-269 deaths per million under ambitious retrofit rates. Annual heat deaths would typically increase by 1 per million per year under the current retrofit rate, and 12-13 per million under ambitious rates without population adaptation to heat. During typical future summers, an estimated 38-73% of heat-related deaths can be avoided using external shutters on windows, with their effectiveness lower during hotter weather. Despite warmer winters, ambitious retrofit rates are necessary to reduce typical annual energy consumption for heating below baseline levels, assuming no improvement in heating system efficiencies. Concerns over future overheating in energy efficient housing are valid but increases in heat attributable mortality during typical and hot (but not extreme) summers are more than offset by significant reductions in cold mortality and easily mitigated using passive measures. More ambitious retrofit rates are critical to reduce energy consumption and offer co-benefits for reducing cold-related mortality.