We introduce a large-scale neurocomputational model of spatial cognition called ’Spacecog’, which integrates recent findings from mechanistic models of visual and spatial perception. As a high-level cognitive ability, spatial cognition requires the processing of behaviourally relevant features in complex environments and, importantly, the updating of this information during processes of eye and body movement. The Spacecog model achieves this by interfacing spatial memory and imagery with mechanisms of object localisation, saccade execution, and attention through coordinate transformations in parietal areas of the brain. We evaluate the model in a realistic virtual environment where our neurocognitive model steers an agent to perform complex visuospatial tasks. Our modelling approach opens up new possibilities in the assessment of neuropsychological data and human spatial cognition.