The explosive Hunga Tonga eruption in 2022 had several characteristics that are unique in the recent observational record. Its effects on the atmosphere are of great scientific interest and have included rapidly propagating patterns of Lamb and gravity waves and long-lived anomalies in stratospheric water vapour. This modelling study demonstrates how, through a coupled sequence of chemical, radiative and dynamical mechanisms, the additional water vapour in the tropical upper stratosphere is likely to have had a significant effect on the wintertime circulation of the stratosphere and hence the troposphere in Northern Hemisphere mid- and high latitudes. These results on the fascinating Hunga Tonga event have wider relevance to perturbations of the climate system where the initial impact is stratospheric but important secondary effects are felt elsewhere, including at the surface.