The Antarctic ice sheet loses mass at its fringes bordering the Southern Ocean. At this boundary, warm circumpolar water can override the continental slope front, reaching the grounding line through submarine glacial troughs and causing high rates of melting at the deep ice-shelf bases. The interplay between ocean currents and continental bathymetry is therefore likely to influence future rates of ice-mass loss. Here we show that a redirection of the coastal current into the Filchner Trough and underneath the Filchner–Ronne Ice Shelf during the second half of the twenty-first century would lead to increased movement of warm waters into the deep southern ice-shelf cavity. Water temperatures in the cavity would increase by more than 2 degrees Celsius and boost average basal melting from 0.2 metres, or 82 billion tonnes, per year to almost 4 metres, or 1,600 billion tonnes, per year. Our results, which are based on the output of a coupled ice–ocean model forced by a range of atmospheric outputs from the HadCM3 climate model, suggest that the changes would be caused primarily by an increase in ocean surface stress in the southeastern Weddell Sea due to thinning of the formerly consolidated sea-ice cover. The projected ice loss at the base of the Filchner–Ronne Ice Shelf represents 80 per cent of the present Antarctic surface mass balance. Thus, the quantification of basal mass loss under changing climate conditions is important for projections regarding the dynamics of Antarctic ice streams and ice shelves, and global sea level rise.