Britain has been a global leader in reducing emissions, but little progress has been made on heat, which accounts for almost one-third of UK emissions and the largest single share is domestic heat, which is responsible for 17% of the national total. Given the UK's 2050 "Net-Zero" commitment, decarbonizing heat is becoming urgent and currently one of the main pathways involves its electrification. Here, we present a spatially explicit optimization model that investigates the implications of electrifying domestic heat on the operation of the power sector. Using hourly historical gas demand data, we conclude that the domestic peak heat demand is almost 50% lower than widely cited values. A 100% electrification pathway can be achieved with only a 1.3-fold increase in generation capacity compared to a power-only decarbonization scenario, but only by leveraging the role of thermal energy storage technologies without which a further 40% increase would be needed.