The 'healthy immigrant effect' and 'migrant mortality advantage' describe the better health and lower mortality of international immigrants as compared with the native-born populations of high-income countries. However, a growing body of evidence suggests that it is much more common to observe low mortality among immigrants than it is good health, pointing to the existence of a potential paradox that mirrors the well-known gender paradox in health and mortality. To investigate this, we used the Office for National Statistics Longitudinal Study, a large-scale representative 1% sample of the England and Wales resident population comprising linked individual-level health, mortality, and socio-demographic data. We compared health and mortality within and across major immigrant groups over 20 years using logistic regression for health and discrete-time survival analysis for mortality, both before and after adjusting for socio-demographic factors. Of the eight origin subgroups studied, we found persistent evidence of a health-mortality paradox within three: men and women from India, Pakistan and Bangladesh, and the Caribbean. We discuss potential explanations and implications of this paradox and suggest that decision makers need to react to help these subgroups preserve their health in order to delay the onset of limiting illnesses and emergence of this paradox.