COVID-19 poses one of the most profound public health crises for a hundred years. As of late March 2020, almost 15,000 deaths and over a quarter of a million confirmed cases have been registered across almost 170 countries or regions. The virus will still infect a sizeable proportion of the world’s population, leading to unprecedented pressures on health care systems. Although national estimates of hospital bed capacity are available, these may obscure important differences at local and regional levels. COVID-19 appears especially dangerous for the oldest age groups and those with serious comorbidities. This makes it crucial to understand how health system capacity matches spatial variation in the underlying population risk. Using England and Wales where the outbreak is currently growing, we illustrate how the interaction of local demography, a high burden of COVID-19 morbidity and mortality at older ages, and regional variation in hospital resources culminates in “hospital deserts” with too few resources to cope with the coming wave of critical cases. Through a stylised example, we demonstrate how local capacity could rapidly become overwhelmed. Understanding more fine-grained local differences in hospitalization capacity supply versus demand can aid in predicting needs for shifting capacity and rapid redistribution of resources.