Directional dispersal plays a large role in shaping ecological processes in diverse systems such as rivers, coastlines and vegetation communities. We describe an instability driven by directional dispersal in a spatially explicit consumer-producer model where spatial patterns emerge in the absence of external environmental variation. Dispersal of the consumer has both undirected and directed components that are functions of producer biomass. We demonstrate that directional dispersal is required for the instability, while undirected diffusive dispersal sets a lower bound to the spatial scale of emerging patterns. Furthermore, instability requires indirect feedbacks affecting consumer per capita dispersal rates, and not activator-inhibitor dynamics affecting production and mortality as is described in previous theory. This novel and less-restrictive mechanism for generating spatial patterns can arise over realistic parameter values, which we explore using an empirically inspired model and data on stream macroinvertebrates.