The Malin Shelf, off north-west Ireland, was an important zone of confluence for marine-based ice streams of the former British-Irish Ice Sheet (BIIS). Legacy geophysical datasets are used to construct models of the seismic character, relative age and distribution of shelf sediments and landforms. Buried and surface landform assemblages provide evidence that during deglaciation of the Late Devensian BIIS, the region was occupied not by a single Hebrides Ice Stream as previously proposed, but by four discrete ice streams, here referred to as the Sea of the Hebrides (SHIS), Inner Hebrides, North Channel and Tory Island ice streams. Our observations of stratigraphic relationships between the deposits of these ice streams indicate physical interactions between them during shelf deglaciation. We interpret an initial dominant cross-shelf flow along the SHIS impeding cross-shelf ice flow from other ice sheet sectors. Following withdrawal of the SHIS grounding line from the shelf edge to mid-shelf bathymetric highs during deglaciation, a reconfiguration of ice sheet flow paths allowed the expansion of smaller cross-shelf ice streams draining central Scotland and north-western Ireland. This internal dynamic behaviour provides a possible physical analogue for time-transgressive flow patterns reported for outlets draining the West Antarctic Ice Sheet.