Summary Observations of postglacial relative sea level (RSL) history at sites beyond the margins of the main accumulations of Wu¨rm–Wisconsin–Devensian ice may be invoked to test the accuracy of global models of the glacial isostatic adjustment process. The existing database of RSL time-series for the British Isles forms a continuous network of sites that sample the coasts of Scotland, England and Wales fairly uniformly, and which may be especially important in this regard. Not only are these 14C data for the Holocene epoch of very high quality in terms of our knowledge of the coastal environment and relationship to palaeo-sea level of each age measurement, but they are especially numerous and relate to an island that was itself partly glaciated in the north, essentially ice-free in the south, and located well outboard of the massive ice-sheet that covered Fennoscandia at the Last Glacial Maximum (LGM). Taken together, the time-series from 55 distinct locations allow us to perform a fairly stringent test of the recently formulated ICE-4G (VM2) global model of the isostatic adjustment process. Even without modification, this model has been shown to fit most of the time-series in the UK data set rather well. In order to satisfy very recently published a priori constraints on the maximum thickness of the Scottish ice-sheet, however, we find that the lithospheric thickness, the feature of the radial viscoelastic structure to which the rebound data from Scotland are most sensitive, must be somewhat reduced. Whereas the assumed thickness of the lithosphere in ICE-4G (VM2) was near to 120 km, best fits to the Scottish data require a lithospheric thickness near to 90 km. This reduced value for lithospheric thickness agrees exceedingly well with the latest estimates of this Earth property based on the inversion of oceanic geoid and topography data, as the asymptotic thickness characteristic of the oldest ocean floor. This would appear to be the best possible a priori estimate for the thickness of the cratonic lithospheres upon which the largest ice-sheets of the late Pleistocene are known to have rested. We also demonstrate explicitly that inferences of the shallow viscoelastic structure beneath the British Isles are strongly influenced by the details of the history of deglaciation at remote locations, at Antarctica in particular.