The dimensions of past ice sheets provide a record of palaeoclimate but depend on underlying topography, which evolves over geological timescales by tectonic uplift and erosional downcutting. Erosion during the Pleistocene epoch (2,580 to 11.650 thousand years ago) reduced glacier extent in some locations even as climate cooled, but whether other non-climatic influences impacted the glacial–geological record is poorly known. The Antarctic Peninsula provides an opportunity to examine this issue because of its long glacial history and preservation of remnants of a low-relief pre-glacial land surface. Here we reconstructed both palaeo-surface topography and long-wavelength variations of surface uplift for the Antarctic Peninsula by using inverse analysis that assimilates local topographic remnants with the branching structures of entire modern drainage networks. We found that the Antarctic Peninsula rose tectonically by up to 1.5 km due to dynamical support from the mantle. Glaciological models using the current climate and our palaeotopography show greatly reduced ice extent in the northern Antarctic Peninsula compared with modern, indicating that the onset of glaciation identified at offshore sites reflects tectonic uplift of the topography rather than climatic cooling. In the southern Antarctic Peninsula, however, we suggest the low-relief pre-glacial landscape supported a considerably greater ice volume than the modern mountainous topography, illustrating the influence of erosional sculpting on glaciation patterns.