The glacial isostatic adjustment (GIA) of the British Isles is complex due to the interplay between local and non-local signals. A number of recent studies have modelled the GIA response of the British Isles using relative sea-level data. This study extends these previous analyses by using output from a numerical glaciological model as input to a GIA model. This is a necessary step towards more realistic GIA models, and although there have been similar studies for the major late Pleistocene ice sheets, this is the first study to do so for the British Isles. We test three reconstructions, classed as ‘minimal’, ‘median’ and ‘maximal’ in terms of their volume at maximum extent, and find it is possible to obtain good data–model fits. The minimal reconstruction is clearly preferred by the sea-level data. The ice reconstructions tested were not constrained by geomorphological information of past ice extent (lateral and vertical). As a consequence, the reconstructions extend further than much of this information suggests, particularly in terms of ice thickness. It is notable, however, that the reconstructions produce good fits to many sea-level data from central, mountainous regions (e.g. Scottish highlands), which lends support to the suggestion that trimlines, often used as an constraint on the palaeo ice surface location, are in fact features formed at the transition from warm- to cold-based ice and so mark a minimum constraint on the ice surface altitude. Based on data–model misfits, suggestions are made for improving the ice model reconstructions. However, in many locations, the cause of the misfit could be due to non-local, predominantly Fennoscandian ice and so interpretation is not straightforward. As a result, we suggest that future analyses of this type consider models and observations for both Fennoscandia and the British Isles. Copyright © 2012 John Wiley & Sons, Ltd.