The wider application of spintronic devices requires the development of new material platforms that can efficiently be used to manipulate spin. Bismuthate-based superconductors are centrosymmetric systems that are generally thought to offer weak spin–orbit coupling. Here we report a large spin–orbit torque driven by spin polarization generated in heterostructures based on the bismuthate BaPb1−xBixO3 (which is in a non-superconducting state). Using spin-torque ferromagnetic resonance and d.c. nonlinear Hall measurements, we measure a spin–orbit torque efficiency of around 2.7 and demonstrate current-driven magnetization switching at current densities of 4 × 105 A cm−2. We suggest that the unexpectedly large current-induced torques could be the result of an orbital Rashba effect associated with local inversion symmetry breaking in BaPb1−xBixO3. © 2023, The Author(s), under exclusive licence to Springer Nature Limited.