The flow of water beneath the Antarctic Ice Sheet has recently been shown to involve drainage from and exchange between subglacial lakes, with flow routing over distances of >100km. As subglacial water is known to be important to ice-sheet dynamics, changes to the flow routing of basal water may yield an ice-sheet response. Here we show that the directions of subglacial hydrological flowpaths are highly sensitive to the ice-sheet surface topography at certain sites in Antarctica. Surface elevation changes, of between 5 and 15 m, are found to be sufficient to produce significant changes to the subglacial water flowpaths, which affect the potential drainage routes of large subglacial lakes. We identify the reasons for this high sensitivity and recognise several locations in East Antarctica where changes to the drainage regime could have important effects on large-scale basal water distribution.