Non-native invasive plants are a widely acknowledged threat to global biodiversity. However, our understanding of the mechanisms underlying plant invasion, and the relative importance of multiple rather than single drivers, remains poor. Here, we provide a case study using time-series data to reconstruct patterns of change, and field experiments to test for causality. We show how, over a 50-year period, a series of unrelated human-induced changes created highly favorable conditions for the non-native tree mallow (Lavatera arborea) to turn invasive, causing loss of native vegetation and seabird breeding habitat. The combination of three drivers: human-introduced disease, climate warming and a fisheries-mediated increase in seabird populations, removed major constraints on plant population growth, (i.e. grazer control, climatic control, germination opportunity and nutrient limitation). Collectively, these changes created optimal conditions for the rapid expansion of tree mallow. The resulting dramatic impact on both the native vegetation and breeding seabirds, notably puffins (Fratercula arctica), exemplifies how non-native invasive plant species can transform terrestrial ecosystems. While climate change is regarded as a key factor behind plant invasion, we highlight that multiple rather than single factors may be critical to biodiversity loss.