The glacial history of the continental shelf northwest of Alexander Island is not well known, due mainly to a lack of targeted marine data on Antarctica’s palaeo-ice sheets in their inter-ice-stream areas. Recently it has been argued that the region was ice-free at the Last Glacial Maximum (LGM) and thus a potential site for glacial refugia. In this paper, multibeam swath bathymetry, sub-bottom profiles and sediment cores are used to map the Alexander Island sector of the Antarctic Peninsula margin, in order to reconstruct the shelf’s palaeoglaciology. Sea-floor bedforms provide evidence that an independent ice cap persisted on Alexander Island through the LGM and deglaciation. We show that this ice cap drained via two major, previously-undescribed tidewater outlets (Rothschild and Charcot Glaciers) sourced from an ice dome centred over the west of the island and near-shore areas. The glaciers grounded along deep, fjord-like cross-shelf troughs to within at least similar to 10-20 km of the shelf edge, and probably reached the shelf break. Only one small outer-shelf zone appears to have remained free of ice throughout an otherwise extensive LGM. During retreat, grounding-line geomorphology indicates periodic stabilisation of Charcot Glacier on the mid-shelf after 13,500 cal yrs BP, while Rothschild Glacier retreated across its mid-shelf by 14,450 cal yrs BP. The timing of these events is in phase with retreat in nearby Marguerite Trough, and we take this as evidence of a common history and forcing with the Antarctic Peninsula Ice Sheet. The fine details of ice flow documented by our new reconstruction highlight the importance of capturing complex ice flow patterns in models (e.g. in inter-stream areas), for understanding how region-specific parts of Antarctica may change in the future. Moreover, the reconstruction shows that glacial refugia, if present, cannot have been extensive on the Alexander Island shelf at the LGM as indicated by previous biological studies; instead, we argue that any ice-free refugia were probably restricted to isolated outer-shelf pockets, that opened, closed, or were maintained through diachronous ice-sheet advance and retreat.