Neuronal responses to similar stimuli change dynamically over time, raising the question of how internal representations can provide a stable substrate for neural coding. Recent work has suggested a large degree of drift in neural representations even in sensory cortices, which are believed to store stable representations of the external world. While the drift of these representations is mostly characterized in relation to external stimuli, the behavioural state of the animal (for instance, the level of arousal) is also known to strongly modulate the neural activity. We therefore asked how the variability of such modulatory mechanisms can contribute to representational changes. We analysed large-scale recording of neural activity from the Allen Brain Observatory, which was used before to document representational drift in the mouse visual cortex. We found that, within these datasets, behavioural variability significantly contributes to representational changes. This effect was broadcasted across various cortical areas in the mouse, including the primary visual cortex, higher order visual areas, and even regions not primarily linked to vision like hippocampus. Our computational modelling suggests that these results are consistent with independent modulation of neural activity by behaviour over slower time scales. Importantly, our analysis suggests that reliable but variable modulation of neural representations by behaviour can be misinterpreted as representational drift, if neuronal representations are only characterized in the stimulus space and marginalised over behavioural parameters.