Population structure is critical to infectious disease transmission. As a result, theoretical and empirical contact networks models of infectious disease spread are increasingly providing valuable insights into wildlife epidemiology. Analysing an exceptionally detailed data set on contact structure within a high-density population of European badgers Meles meles, we show that a modular contact network produced by spatially structured stable social groups, lead to smaller epidemics, particularly for infections with intermediate transmissibility. The key advance is that we identify considerable variation among individuals in their role in disease spread, with these new insights made possible by the detail in the badger data set. Furthermore, the important impacts on epidemiology are found even though the modularity of the badger network is much lower than the threshold that previous work suggested was necessary. These findings reveal the importance of stable social group structure for disease dynamics with important management implications for socially-structured populations.