Climate change influences population demography by altering patterns of gene flow and reproductive isolation. Direct mutation rates offer the possibility for accurate dating on the within-species level but are currently only available for a handful of vertebrate species. Here, we use the first directly estimated mutation rate in birds to study the evolutionary history of pied flycatchers (Ficedula hypoleuca). Using a combination of demographic inference and species distribution modelling, we show that all major population splits in this forest-dependent system occurred during periods of increased climate instability and rapid global temperature change. We show that the divergent Spanish subspecies originated during the Eemian-Weichselian transition 115-104 thousand years ago (kya), and not during the last glacial maximum (26.5-19 kya), as previously suggested. The magnitude and rates of climate change during the glacial-interglacial transitions that preceded population splits in pied flycatchers were similar to, or exceeded, those predicted to occur in the course of the current, human-induced climate crisis. As such, our results provide a timely reminder of the strong impact that episodes of climate instability and rapid temperature changes can have on species' evolutionary trajectories, with important implications for the natural world in the Anthropocene.