Many normal and pathological biological processes involve the migration of epithelial cell sheets. This arises from complex emergent behaviour resulting from the interplay between cellular signalling networks and the forces that physically couple the cells. Here, we demonstrate that collective migration of an epithelium can be interactively guided by applying electric fields that bias the underlying signalling networks. We show that complex, spatiotemporal cues are locally interpreted by the epithelium, resulting in rapid, coordinated responses such as a collective U-turn, divergent migration, and unchecked migration against an obstacle. We observed that the degree of external control depends on the size and shape of the cell population, and on the existence of physical coupling between cells. Together, our results offer design and engineering principles for the rational manipulation of the collective behaviour and material properties of a tissue.