Within the standard hierarchical structure formation scenario, Milky Way-mass dark matter haloes have hundreds of dark matter subhaloes with mass ≳ 108 M⊙. Over the lifetime of a galactic disc, a fraction of these may pass close to the central region and interact with the disc. We extract the properties of subhaloes, such as their mass and trajectories, from a realistic cosmological simulation to study their potential effect on stellar discs. We find that massive subhalo impacts can generate disc heating, rings, bars, warps, lopsidedness as wells as spiral structures in the disc. Specifically, strong counter-rotating single-armed spiral structures form each time a massive subhalo passes through the disc. Such single-armed spirals wind up relatively quickly (over  1–2  Gyr) and are generally followed by corotating two-armed spiral structures that both develop and wind up more slowly. In our simulations, self-gravity in the disc is not very strong and these spiral structures are found to be kinematic density waves. We demonstrate that there is a clear link between each spiral mode in the disc and a given subhalo that caused it, and by changing the mass of the subhalo, we can modulate the strength of the spirals. Furthermore, we find that the majority of subhaloes interact with the disc impulsively, such that the strength of spirals generated by subhaloes is proportional to the total torque they exert. We conclude that only a handful of encounters with massive subhaloes are sufficient for regenerating and sustaining spiral structures in discs over their entire lifetime.