The British and Irish Ice Sheet (BIIS) was highly dynamic during the Late Quaternary, with considerable regional differences in the timing and extent of its change. This was reflected in equally variable offshore ice‐rafted debris (IRD) records. Here we reconcile these two records using the FRUGAL intermediate complexity iceberg–climate model, with varying BIIS catchment‐level iceberg fluxes, to simulate change in IRD origin and magnitude along the western European margin at 1000‐year time steps during the height of the last BIIS glaciation (31–6 ka bp). This modelled IRD variability is compared with existing IRD records from the deep ocean at five cores along this margin. There is general agreement of the temporal and spatial IRD variability between observations and model through this period. The Porcupine Bank off northwestern Ireland was confirmed by the modelling as a major dividing line between sites possessing exclusively northern or southern source regions for offshore IRD. During Heinrich events 1 and 2, the cores show evidence of a proportion of North American IRD, more particularly to the south of the British Isles. Modelling supports this southern bias for likely Heinrich impact, but also suggests North American IRD will only reach the British margin in unusual circumstances.