Conservation planners often wish to predict how species distributions will change in response to environmental changes. Species distribution models (SDMs) are the primary tool for making such predictions. Many methods are widely used; however, they all make simplifying assumptions, and predictions can therefore be subject to high uncertainty. With global change well underway, field records of observed range shifts are increasingly being used for testing SDM transferability. We used an unprecedented distribution dataset documenting recent range changes of British vascular plants, birds, and butterflies to test whether correlative SDMs based on climate change provide useful approximations of potential distribution shifts. We modelled past species distributions from climate using nine single techniques and a consensus approach, and projected the geographical extent of these models to a more recent time period based on climate change; we then compared model predictions with recent observed distributions in order to estimate the temporal transferability and prediction accuracy of our models. We also evaluated the relative effect of methodological and taxonomic variation on the performance of SDMs. Models showed good transferability in time when assessed using widespread metrics of accuracy. However, models had low accuracy to predict where occupancy status changed between time periods, especially for declining species. Model performance varied greatly among species within major taxa, but there was also considerable variation among modelling frameworks. Past climatic associations of British species distributions retain a high explanatory power when transferred to recent time--due to their accuracy to predict large areas retained by species--but fail to capture relevant predictors of change. We strongly emphasize the need for caution when using SDMs to predict shifts in species distributions: high explanatory power on temporally-independent records--as assessed using widespread metrics--need not indicate a model's ability to predict the future.