Sedimentary basins beneath many Antarctic ice streams host substantial volumes of groundwater, which can be exchanged with a “shallow” subglacial hydrological system of till and channelised water. This exchange contributes substantially to basal water budgets, which in turn modulate the flow of ice streams. The geometry of these sedimentary basins is known to be complex, and the groundwater therein has been observed to vary in salinity due to historic seawater intrusion. However, little is known about the hydraulic properties of subglacial sedimentary basins, and the factors controlling groundwater exfiltration and infiltration. We develop a mathematical model for two-dimensional groundwater flow beneath a marine-terminating ice stream on geological timescales, taking into account the effect of seawater intrusion. We find that seawater may become “trapped” in subglacial sedimentary basins, through cycles of grounding line advance and retreat or through “pockets” arising from basin geometry. In addition, we estimate the sedimentary basin permeability which reproduces field observations of groundwater salinity profiles from beneath Whillans Ice Stream in West Antarctica. Exchange of groundwater with the shallow hydrological system is primarily controlled by basin geometry, with groundwater being exfiltrated where the basin becomes shallower and re-infiltrating where it becomes deeper. However, seawater intrusion also has non-negligible effects on this exchange.