Confidence in projections of the future distributions of species requires demonstration that recently-observed changes could have been predicted adequately. Here we use a dynamic model framework to demonstrate that recently-observed changes at the expanding northern boundaries of three British butterfly species can be predicted with good accuracy. Previous work established that the distributions of the study species currently lag behind climate change, and so we presumed that climate is not currently a major constraint at the northern range margins of our study species. We predicted 1970–2000 distribution changes using a colonisation model, MIGRATE, superimposed on a high-resolution map of habitat availability. Thirty-year rates and patterns of distribution change could be accurately predicted for each species (κ goodness-of-fit of models >0.64 for all three species, corresponding to >83% of grid cells correctly assigned), using a combination of individual species traits, species-specific habitat associations and distance-dependent dispersal. Sensitivity analyses showed that population productivity was the most important determinant of the rate of distribution expansion (variation in dispersal rate was not studied because the species are thought to be similar in dispersal capacity), and that each species’ distribution prior to expansion was critical in determining the spatial pattern of the current distribution. In future, modelling approaches that combine climate suitability and spatially-explicit population models, incorporating demographic variables and habitat availability, are likely to be valuable tools in projecting species’ responses to climatic change and hence in anticipating management to facilitate species’ dispersal and persistence.