The glacial isostatic adjustment (GIA) of the British Isles is of interest due to the constraints that can be provided on key model parameters such as the global meltwater signal, local ice sheet history and viscoelastic earth structure. A number of recent studies have modelled relative sea-level (RSL) data from this region to constrain model parameters. As indicated in these studies, the sensitivity of these data to both local and global parameters results in a highly non-unique problem. This study aims to address this inherent non-uniqueness by combining a previously published British–Irish ice model that is based on the most recent geomorphological data with a new global ice sheet model that provides an accurate prediction of eustatic sea-level change. In addition, constraints from Global Positioning System (GPS) measurements of present-day vertical land motion are considered alongside the entirety of RSL data from both Great Britain and Ireland. A model solution is found that provides a high-quality fit to both the RSL data and the GPS data. Within the range of earth viscosity values considered, the optimal data model fits were achieved with a relatively thin lithosphere (71 km), upper mantle viscosities in the range 4–6 × 1020 Pa s and lower mantle viscosities ≥ 3 × 1022 Pa s. Copyright © 2011 John Wiley & Sons, Ltd.