The topographies of Africa and Antarctica form patterns of interlocking swells. The relationship between topography and gravity indicates that these swells are dynamically supported by mantle convection, with swell diameters of 1850 ± 450 km and full heights between 800 and 1800 m. The implication is that mantle convection not only supports swells surrounding hotspots but also influences topography across the entire surface areas of Africa and Antarctica. We investigate whether dynamically supported swells are also observed throughout the geological record, focusing on intensively studied Mesozoic–Cenozoic sedimentary rocks around Britain and Ireland. Vertical motions of Britain and Ireland, a typical piece of continental lithosphere far from a destructive plate boundary, have been demonstrably affected by dynamic support for over half of the past 200 Ma period. The diameters and maximum heights of the Mesozoic British swells and the modern African and Antarctic swells are similar. The ancient British swells grew in 5–10 Ma and decayed over 20–30 Ma, suggesting vertical motion rates comparable with those estimated from geomorphological studies of Africa. Igneous production rate and swell height are not correlated in the modern and the geological records. Mantle convection should be considered as a common control on regional sea level.