Observations of relative sea-level (RSL) change in Great Britain since 16 kyr BP and models of post-glacial isostatic adjustment provide constraints on reconstructions of the British and Antarctic ice sheets from the Last Glacial Maximum to the present. We use the global model from an earlier investigation, modified ICE-4G (VM2) with lithospheric thickness=90 km, which gives good RSL fits globally as well as for much of the British data. A revised ice model for Great Britain that fits with recently published observations on ice limits and heights fails to explain all the misfits between RSL observations and predictions. Much more significant improvements result from models that incorporate a different chronology for the partial deglaciation of Antarctica, while keeping the total ice melt, ∼17 m, the same as in ICE-4G (VM2). The results suggest Antarctic melting of ∼3 m ice equivalent sea level by 15 kyr BP, only ∼1 m contribution to the ∼24 m rise of MWP1a, with the major melting 12–5 kyr BP, and a small amount of melting, 1.0±0.3 m, between then and 3 or 2 kyr BP. These modifications produce RSL predictions for Barbados that show the major changes in rate of sea level rise, but with an offset up to 1 kyr compared to the observations. Possible explanations that remain to be investigated further are a delay in the melting of ice from some other region, a reduction in the total melt derived from Antarctica, and a refinement of the 1 kyr temporal resolution assumed in the construction of the theoretical solution.