The Antarctic Circumpolar Current is key to the mixing and ventilation of the world’s oceans. This current flows from west to east between about 45° and 70°S connecting the Atlantic, Pacific and Indian oceans, and is driven by westerly winds and buoyancy forcing. High levels of productivity in the current regulate atmospheric CO2 concentrations. Reconstructions of the current during the last glacial period suggest that flow speeds were faster or similar to present, and it is uncertain whether the strength and position of the westerly winds changed. Here we reconstruct Antarctic Circumpolar Current bottom speeds through the constricting Drake Passage and Scotia Sea during the Last Glacial Maximum and Holocene based on the mean grain size of sortable silt from a suite of sediment cores. We find essentially no change in bottom flow speeds through the region, and, given that the momentum imparted by winds, and modulated by sea-ice cover, is balanced by the interaction of these flows with the seabed, this argues against substantial changes in wind stress. However, glacial flow speeds in the sea-ice zone south of 56°S were significantly slower than present, whereas flow in the north was faster, but not significantly so. We suggest that slower flow over the rough topography south of 56°S may have reduced diapycnal mixing in this region during the last glacial period, possibly reducing the diapycnal contribution to the Southern Ocean overturning circulation.