Uncertainties in future sea level projections are dominated by our limited understanding of the dynamical processes that control instabilities of marine ice sheets. The last deglaciation of the British-Irish Ice Sheet offers a valuable example to examine these processes. 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 constrained with abundant empirical data which can 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 perform simplified experiments of the retreat of this ice stream under an idealised climate forcing to isolate the effect of marine ice sheet processes, simulating retreat from the continental shelf under constant "warm" surface mass balance and sub-ice-shelf melt. The model simulates a slowdown of retreat as the ice stream becomes laterally confined at the mouth of the Minch strait between mainland Scotland and the Isle of Lewis, resulting in a marine setting similar to many large tidewater glaciers in Greenland and Antarctica. At this stage of the simulation, the presence of an ice shelf becomes a more important control on grounded ice volume, 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. We conclude that geological data could be applied to further constrain these processes in ice sheet models used for projecting the future of contemporary ice sheets.