Summertime overheating in dwellings in temperate climates is widespread. Overheating in bedrooms disrupts sleep, degrading health and wellbeing, and can be life-threatening. Air-conditioning homes is a solution, but is expensive and adds load onto electricity networks. An alternative is to provide safe havens, a cool retreat for sleeping when the main bedroom overheats. This paper estimates the number of English dwellings that might already have such spaces. The 2017 Energy Follow Up Survey (EFUS) to the English Housing Survey (EHS) provides temperatures measured in the main bedroom, up to two other bedrooms and the living room of 750 homes. These data were collected in 2018, a summer typical of those expected in the 2050s. The main bedroom overheated in 19% of the housing stock as judged by an adaptive comfort criterion. Up to 76% of these homes had living rooms that could provide a safe haven, and in up to 46% an alternative bedroom might provide a safe haven. Very few, if any, flats and small-area dwellings had a safe haven. These figures provide an upper-bound estimate; in practice the useable number of safe havens is likely to be less. <em><strong>Policy relevance</strong></em> Safe havens for use during heatwaves have been suggested as a climate-adaptive strategy to ameliorate indoor overheating. In this study, the prevalence of safe havens, which can be slept in when the main bedroom overheats, is estimated. Living rooms offered the best opportunity of a safe haven for sleeping, with 5.8 million of the 7.4 million people experiencing an overheated main bedroom being relieved of exposure. Flats and small dwellings were more prone to overheating, but few, if any, had either a living room or a spare bedroom that offered a safe haven. Overall, this study strengthens the idea that public health advice, especially during heatwaves, should be tailored to different dwelling and household types. For larger dwellings other than flats, advice could emphasise the benefits of sleeping in the living room, where possible, on hot nights. Homes without safe havens should be the focus of heat mitigation retrofit strategies.