We study the joint evolution of the distributions of health and wealth under household level shocks to health and income, and uncertainty about disease outbreaks. We specify a model in which health and wealth are jointly determined, under idiosyncratic income and health risk that is related to disease outbreak risk. We calibrate the model to a number of properties of the pre-COVID-19 UK health and income distributions, including the social mobility matrix and differences in mean health and in health and labour income risk by professional class. We use the model to study the likely medium-run wealth and health inequality implications of the COVID-19 pandemic in the UK, and find that the majority of future time paths imply significant increases in both wealth and health inequality.