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In many countries, wintertime cold weather is linked to ill-health and intense pressure on public health services. This study examines how both long-term climate change and sub-seasonal variability contribute to the temperature extremes that increase pressures on the UK's National Health Service. The impact of temperature on fractional mortality and hospital admissions due to chronic obstructive pulmonary disease are used as metrics of wintertime pressure on the health system. The focus of the study is on days during the year in which the fractional mortality and hospital admissions attributable to cold weather exceed the five-year return period. These days are henceforth called winter pressure days since they likely to lead to significant pressure on the health service to meet demand. On interdecadal and longer timescales, winter pressure days show a robust decline over recent decades with a reduction from a probability of 0.29 in the pre-industrial period to 0.11 for the period 2000-2016. Comparing the risk of winter pressure days in two different climate model simulations of the historical period and a counterfactual ensemble of only natural climate forcings shows that this decline can be clearly attributed to anthropogenic activity. The average Fraction of Attributable risk due to anthropogenic activity for these two climate models for winter pressure days is -0.94. On sub-seasonal timescales, weather drivers of winter pressure days are assessed through analysis of diagnostics of weather regime lifecycles. This analysis shows winter pressure days occur almost exclusively in the Greenland Blocking regime. Although the risk of winter pressure days is likely to continue to decline with current climate trends, there remains a substantial weather driven risk to the UK health system. Preparing for weather events that cause stress on the system should focus on the analysis and prediction of the Greenland Blocking regime on weekly timescales.