Sea-ice control on deglacial lower cell circulation changes recorded by Drake Passage deep-sea corals

•First direct constraints on past water mass mixing in Lower Circumpolar Deep Water.•Reduced North Atlantic Deep Water signal in deep Southern Ocean during peak glacial.•Control by Southern Ocean stratification rather than Atlantic overturning strength.•Early deglacial Southern Ocean circulation changes linked to sea-ice retreat.•Spatially asynchronous return of North Atlantic Deep Water to deep South Atlantic.