This paper assesses the extent to which a topographically defined description of the spatial arrangement of catchment wetness can be used to represent landscape hydrological connectivity in temperate river catchments. A physically based distributed hydrological model is used to characterize the space‐time patterns of surface overland flow connection to the drainage network. These characterizations are compared with a static descriptor of the spatial structure of topographically controlled local wetness, called here the Network Index. Theoretically, if topography is the primary control upon hydrological response, the level of catchment wetness required to maintain connectivity along a flow path should be greater for flow paths that have a lower value of the topographically controlled local wetness. We find that our static descriptor can be used to generalize a significant proportion of the time‐averaged spatial variability in connectivity, in terms of both the propensity to and duration of connection. Although the extent to which this finding holds will vary with the extent of topographic control of hydrological response, in catchments with relatively shallow soils and impervious geology our index could improve significantly the estimation of the transfer of sediment and dissolved materials to the drainage network and so assist with both diffuse pollution and climate change impact studies. The work also provides a second reason for the concept that there are Critical Source Areas in river catchments: these arise from the extent to which that material can be delivered to the drainage network, as well as the generation of risky material itself.