Strategies to reduce domestic heating loads by minimizing the infiltration of cold air through adventitious openings located in the thermal envelopes of houses are highlighted by the building codes of many countries. Consequent reductions of energy demand and CO<inf>2</inf>e emission are often unquantified by empirical evidence. Instead, a mean heating season infiltration rate is commonly inferred from an air leakage rate using a simple ratio scaled to account for the physical and environmental properties of a dwelling. The scaling does not take account of the permeability of party walls in conjoined dwellings and so cannot differentiate between the infiltration of unconditioned ambient air that requires heating, and conditioned air from adjacent dwellings that does not.A stochastic method is presented that applies a theoretical model of adventitious infiltration to predict distributions of mean infiltration rates and the associated total heat loss in any stock of dwellings during heating hours. The method is applied to the English and UK housing stocks and provides probability distribution functions of stock infiltration rates and total heat loss during the heating season for two extremes of party wall permeability. The distributions predict that up to 79% of the current English stock could require additional purpose-provided ventilation to limit negative health consequences. National models predict that fewer dwellings are under-ventilated. The distributions are also used to predict that infiltration is responsible for 3-5% of total UK energy demand, 11-15% of UK housing stock energy demand, and 10-14% of UK housing stock carbon emissions.