The demographic structure of populations in both more developed and less developed countries is changing: increases in life expectancy and declining fertility have led to older populations and smaller households. The implications of these demographic changes for the spread and control of infectious diseases are not fully understood. Here we use an individual based model with realistic and dynamic age and household structure to demonstrate the marked effect that demographic change has on disease transmission at the population and household level. The decline in fertility is associated with a decrease in disease incidence and an increase in the age of first infection, even in the absence of vaccination or other control measures. Although large households become rarer as fertility decreases, we show that there is a proportionate increase in incidence of disease in these households as the accumulation of susceptible clusters increases the potential for explosive outbreaks. By modelling vaccination, we provide a direct comparison of the relative importance of demographic change and vaccination on incidence of disease. We highlight the increased risks associated with unvaccinated households in a low fertility setting if vaccine behaviour is correlated with household membership. We suggest that models that do not account for future demographic change, and especially its effect on household structure, may potentially overestimate the impact of vaccination.