Uncertainties in future sea level projections are dominated by our limited understanding of the dynamical processes that control instabilities of marine ice sheets. A valuable case to examine these processes is the last deglaciation of the British-Irish Ice Sheet. The Minch Ice Stream, which drained a large proportion of ice from the northwest sector of the British-Irish Ice Sheet during the last deglaciation, is well constrained, with abundant empirical data which could be used to inform, validate and analyse numerical ice sheet simulations. We use BISICLES, a higher-order ice sheet model, to examine the dynamical processes that controlled the retreat of the Minch Ice Stream. We simulate retreat from the shelf edge under constant "warm" surface mass balance and subshelf melt, to isolate the role of internal ice dynamics from external forcings. The model simulates a slowdown of retreat as the ice stream becomes laterally confined at a "pinning-point" between mainland Scotland and the Isle of Lewis. At this stage, the presence of ice shelves became a major control on deglaciation, providing buttressing to upstream ice. Subsequently, the presence of a reverse slope inside the Minch Strait produces an acceleration in retreat, leading to a "collapsed" state, even when the climate returns to the initial "cold" conditions. Our simulations demonstrate the importance of the Marine Ice Sheet Instability and ice shelf buttressing during the deglaciation of parts of the British-Irish Ice Sheet. Thus, geological data could be used to constrain these processes in ice sheet models used for projecting the future of our contemporary ice sheets. Funding was provided by the Natural Environment Research Council (NERC) SPHERES Doctoral Training Partnership (NE/L002574/1) with CASE support from the British Geological Survey.