Flux-ratio anomalies in quasar lenses can be attributed to dark matter substructure surrounding the lensing galaxy and thus used to constrain the substructure mass fraction. Previous applications of this approach infer a substructure abundance that is potentially in tension with the predictions of Λ cold dark matter cosmology. However, the assumption that all flux-ratio anomalies are due to substructure is a strong one and alternative explanations have not been fully investigated. Here, we use new high-resolution near-IR Keck II adaptive optics imaging for the lens system CLASS B0712+472 to perform pixel-based lens modelling for this system and, in combination with the new Very Long Baseline Array radio observations, show that the inclusion of the disc in the lens model can explain the flux-ratio anomalies without the need for dark matter substructures. The projected disc mass comprises 16 per cent of the total lensing mass within the Einstein radius and the total disc mass is 1.79 × 10^10 M_⊙. The case of B0712+472 adds to the evidence that not all flux-ratio anomalies are due to dark subhaloes and highlights the importance of taking the effects of baryonic structures more fully into account in order to obtain an accurate measure of the substructure mass fraction.