A combination of glaciological theory and geological observations was used to investigate the possibility of till consolidation being driven by basal freeze‐on beneath a stagnating, mid‐latitude palaeo‐ice stream. We focused on the case of the Baltic Ice Stream that advanced into Denmark at c. 15ka BP and which left behind a characteristic till sequence consisting of a strong and well‐consolidated till crust underlain by weak and poorly consolidated till. Our hypothesis is that basal freezing caused the markedly higher consolidation of the uppermost till layer. The freezing may have either triggered or simply just accompanied ice‐stream stoppage. To test the feasibility of this hypothesis, we have developed a numerical model that couples ice‐stream dynamics to time‐dependent changes of till properties. Despite relatively mild palaeo‐climatic conditions in this area during Late Pleistocene deglaciation (˜0°C), the ice‐stream model is capable of producing basal freezing when the effect of horizontal advection of cold ice is included. Our simulations of till response to basal freezing are based on thermodynamic concepts adapted from permafrost studies. Dewatering of till by basal freeze‐on may lead to overconsolidation (OCR>10). Based on the history of effective pressure changes in the till, we can predict postglacial till strength profiles using the SHANSEP method. In a series of numerical experiments we have examined the response of till strength to basal freeze‐on induced beneath a decaying ice sheet. We have come reasonably close to reproducing shear strength profiles for till deposited by the Baltic Ice Stream. These observations are most consistent with palaeo‐ice‐stream stagnation triggered by basal freezing and followed by abrupt retreat (<100 years) due to high surface ablation rates (>10 ma‐1).