Current ice loss from the West Antarctic Ice Sheet (WAIS) accounts for about ten per cent of observed global sea-level rise. Losses are dominated by dynamic thinning, in which forcings by oceanic or atmospheric perturbations to the ice margin lead to an accelerated thinning of ice along the coastline. Although central to improving projections of future ice-sheet contributions to global sea-level rise, the incorporation of dynamic thinning into models has been restricted by lack of knowledge of basal topography and subglacial geology so that the rate and ultimate extent of potential WAIS retreat remains difficult to quantify. Here we report the discovery of a subglacial basin under Ferrigno Ice Stream up to 1.5 kilometres deep that connects the ice-sheet interior to the Bellingshausen Sea margin, and whose existence profoundly affects ice loss. We use a suite of ice-penetrating radar, magnetic and gravity measurements to propose a rift origin for the basin in association with the wider development of the West Antarctic rift system. The Ferrigno rift, overdeepened by glacial erosion, is a conduit which fed a major palaeo-ice stream on the adjacent continental shelf during glacial maxima. The palaeo-ice stream, in turn, eroded the 'Belgica' trough, which today routes warm open-ocean water back to the ice front to reinforce dynamic thinning. We show that dynamic thinning from both the Bellingshausen and Amundsen Sea region is being steered back to the ice-sheet interior along rift basins. We conclude that rift basins that cut across the WAIS margin can rapidly transmit coastally perturbed change inland, thereby promoting ice-sheet instability.