Accurate measurement of the temporal and spatial variation of uplift and denudation would improve our understanding of the way in which mountain building and mantle convection modify the Earth's surface. Here, we show that inverse modeling of stacking velocity data from seismic reflection data sets is a potentially useful tool for obtaining spatially resolved denudation estimates along and across continental shelves. Unlike many techniques for measuring denudation, our approach is not restricted to outcrop or borehole locations, although it is important to calibrate results with other measurements of denudation. We have inverted 2200 stacking velocity analyses from a dense network of two-dimensional seismic reflection lines which surround the British Isles. This region was chosen because there is a well-known signal of Cenozoic uplift and denudation which is big enough to be detectable using our approach. Despite simplified assumptions about the way in which porosity varies with depth, our offshore denudation estimates are consistent with outcrop patterns and accord with published denudation measurements. Furthermore, stacking velocity estimates agree with measurements obtained by analyzing sonic velocity logs from selected boreholes. A region encompassing the British Isles has evidently undergone variable amounts of denudation during Cenozoic times. However, significant denudation (>1.5 km) is concentrated in discrete areas, such as off NW Scotland and parts of the Irish Sea. The magnitude of denudation changes significantly over short (~10 km) distances, implying that differential uplift and erosion have been important factors in creating the present-day denudation pattern.