Abstract The hippocampus has long been observed to encode a representation of an animal’s position in space. Recent evidence suggests that the nature of this representation is somewhat predictive and can be modelled by learning a successor representation (SR) between distinct positions in an environment. However, this discretisation of space is subjective making it difficult to formulate predictions about how some environmental manipulations should impact the hippocampal representation. Here we present a model of place and grid cell firing as a consequence of learning a SR from a basis set of known neurobiological features – boundary vector cells (BVCs). The model describes place cell firing as the successor features of the SR, with grid cells forming a low-dimensional representation of these successor features. We show that the place and grid cells generated using the BVC-SR model provide a good account of biological data for a variety of environmental manipulations, including dimensional stretches, barrier insertions, and the influence of environmental geometry on the hippocampal representation of space.