We present results from a suite of forward transient numerical modelling experiments of the British and Irish Ice Sheet (BIIS), consisting of Scottish, Welsh and Irish accumulation centres, spanning the last Glacial period from 38 to 10 ka BP. The 3D thermomechanical model employed uses higher-order physics to solve longitudinal (membrane) stresses and to reproduce grounding-line dynamics. Surface mass balance is derived using a distributed degree-day calculation based on a reference climatology from mean (1961–1990) precipitation and temperature patterns. The model is perturbed from this reference state by a scaled NGRIP oxygen isotope curve and the SPECMAP sea-level reconstruction. Isostatic response to ice loading is computed using an elastic lithosphere/relaxed asthenosphere scheme. A suite of 350 simulations were designed to explore the parameter space of model uncertainties and sensitivities, to yield a subset of experiments that showed close correspondence to offshore and onshore ice-directional indicators, broad BIIS chronology, and the relative sea-level record. Three of these simulations are described in further detail and indicate that the separate ice centres of the modelled BIIS complex are dynamically interdependent during the build up to maximum conditions, but remain largely independent throughout much of the simulation. The modelled BIIS is extremely dynamic, drained mainly by a number of transient but recurrent ice streams which dynamically switch and fluctuate in extent and intensity on a centennial time-scale. A series of binge/purge, advance/retreat, cycles are identified which correspond to alternating periods of relatively cold-based ice, (associated with a high aspect ratio and net growth), and wet-based ice with a lower aspect ratio, characterised by streaming. The timing and dynamics of these events are determined through a combination of basal thermomechanical switching spatially propagated and amplified through longitudinal coupling, but are modulated and phase-lagged to the oscillations within the NGRIP record of climate forcing. Phases of predominant streaming activity coincide with periods of maximum ice extent and are triggered by abrupt transitions from a cold to relatively warm climate, resulting in major iceberg/melt discharge events into the North Sea and Atlantic Ocean. The broad chronology of the modelled BIIS indicates a maximum extent at ∼20 ka, with fast-flowing ice across its western and northern sectors that extended to the continental shelf edge. Fast-flowing streams also dominate the Irish Sea and North Sea Basin sectors and impinge onto SW England and East Anglia. From ∼19 ka BP deglaciation is achieved in less than 2000 years, discharging the freshwater equivalent of ∼2 m global sea-level rise. A much reduced ice sheet centred on Scotland undergoes subsequent retrenchment and a series of advance/retreat cycles into the North Sea Basin from 17 ka onwards, culminating in a sustained Younger Dryas event from 13 to 11.5 ka BP. Modelled ice cover is persistent across the Western and Central Highlands until the last remnant glaciers disappear around 10.5 ka BP.