Aims. I attempt to fully understand the origin of the stellar and substellar populations in the young σ Orionis open cluster, which is a benchmark for star-forming studies. Because of the very low proper motion of the cluster, late-type dwarfs with appreciable proper motion in the foreground of σ Orionis can be easily discarded as targets from expensive spectroscopic follow-up studies. Methods. I use the Aladin sky atlas, USNO-B1, public astrometric catalogues, and photographic plate digitisations to identify stars with proper motions that are inconsistent with cluster membership in a circular area of radius 30 arcmin centred on the early-type multiple system σ Ori. Primarily because of the long time baseline of more than half a century, the errors in the measured proper motions are lower than 2 mas a −1 . Results. Of the 42 stars selected for astrometric follow-up, 37 of them are proper-motion cluster interlopers. Some USNO-B1 measurements were affected by partially resolved (visual) multiplicity and target faintness. Because of their late spectral types and, hence, red colours, 24 contaminants had been considered at some point as σ Orionis members. I discuss how contamination may have affected previous work (especially related to disc frequencies) and the curious presence of lithium absorption in three M-dwarf proper motion contaminants. Finally, I classify the bright star HD 294297 as a late-F field dwarf unrelated to the cluster based on a new proper motion measurement. Conclusions. Although proper motions cannot be used to confirm membership in σ Orionis, they can be instead used to discard a number of cluster member candidates without spectroscopy.