Abstract Global sea-level rise caused by a warming climate increases flood risk from storm surge events for those who live in coastal and low-lying areas. Estimates of global thermosteric sea-level rises are well constrained by model projections, but local variability in dynamic sea-level arising from seasonal and interannual changes is less well characterised. In this paper we use satellite altimetry observations coupled with CMIP6 model projections to understand drivers of change in dynamic sea-level over the UK shelf seas. We find a northward shift in the atmospheric jet stream and a weakening of the Atlantic meridional overturning circulation to be the key drivers of local dynamic sea-level variability. Using a storyline approach to constrain climate system responses to changes in atmospheric greenhouse gas concentrations, we find that dynamic sea-level is predicted to rise between 15–39 cm by 2080–2099 along the east coast of England (ECE). Under a worst-case scenario, assuming maximum variability as seen in the CMIP6 projections, ECE dynamic sea-level rise could reach 58 cm by 2100. We illustrate the impact of this dynamic sea-level rise in addition to non-dynamic components on the risks posed by storm surge events in ECE using an idealised example. If a storm surge event of the magnitude of the one experienced in ECE on the 5th of December 2013 was to occur in 2100, an additional 1414 km² of land would potentially be affected in our worst-case idealised example, 22.4% of which can be attributed to dynamic sea-level rise.