We study the influence of synoptic scale atmospheric circulation on extreme daily precipitation across the United Kingdom, using observed time series from 689 rain gauges. To this end we employ a statistical model, that uses airflow strength, direction and vorticity as predictors for the generalised extreme value distribution of monthly precipitation maxima. The inferred relationships are connected with the dominant westerly flow, the orography, and the moisture supply from surrounding seas. We aggregated the results for individual rain gauges to regional scales to investigate the temporal variability of extreme precipitation. Airflow explains a significant fraction of the variability on subannual to decadal time scales. A large fraction of the especially heavy winter precipitation during the 1980s and 1990s in north Scotland can be attributed to a prevailing positive phase of the North Atlantic Oscillation. Our statistical model can be used for statistical downscaling and to validate regional climate model output.