ABSTRACT Observational estimates of the lifetimes and inferred accretion rates from debris discs around polluted white dwarfs are often inconsistent with the predictions of models of shielded Poynting–Robertson drag on the dust particles in the discs. Moreover, many cool polluted white dwarfs do not show any observational evidence of accompanying discs. This may be explained, in part, if the debris discs had shorter lifetimes and higher accretion rates than predicted by Poynting–Robertson drag alone. We consider the role of a magnetic field on tidally disrupted diamagnetic debris and its subsequent effect on the formation, evolution, and accretion rate of a debris disc. We estimate that magnetic field strengths greater than ∼10 kG may decrease the time needed for circularization and the disc lifetimes by several orders of magnitude and increase the associated accretion rates by a similar factor, relative to Poynting–Robertson drag. We suggest some polluted white dwarfs may host magnetic fields below the typical detectable limit and that these fields may account for a proportion of polluted white dwarfs with missing debris discs. We also suggest that diamagnetic drag may account for the higher accretion rate estimates among polluted white dwarfs that cannot be predicted solely by Poynting–Robertson drag and find a dependence on magnetic field strength, orbital pericentre distance, and particle size on predicted disc lifetimes and accretion rates.