This paper investigates the future of human longevity, morbidity and health costs in a novel, multi-period overlapping generations model with endogenous medical R&D and endogenous survival that is closely associated with morbidity. We capture biologically founded ageing based on gerontology research in order to calibrate our model for the UK. The baseline policy scenario of health care access suggests substantial future increases in human longevity that are associated with both reductions in morbidity and a rising health expenditure share in GDP. Stabilizing the health expenditure share by rationing health care has potentially sizable effects on morbidity and longevity in the longer run, associated with reduced medical R&D incentives. The implied welfare effects may be substantially negative particularly for future generations.