We present linear spectropolarimetric data for eight Herbig Be and four Herbig Ae stars at Hα, Hβ and Hγ. Changes in the linear polarization are detected across all Balmer lines for a large fraction of the observed objects, confirming that the small-scale regions surrounding these objects are flattened (i.e. disc-like). Furthermore, all objects with detections show similar characteristics at the three spectral lines, despite differences in transition probability and optical depth going from Hα to Hγ. A large fraction of early Herbig Be stars (B0–B3) observed show line-depolarization effects. However, the early Herbig Ae stars (A0–A2), observed for comparison, show intrinsic line-polarization signatures. Our data suggest that the popular magnetic accretion scenario for T Tauri objects may be extended to Herbig Ae stars, but that it may not be extended to early Herbig Be stars, for which the available data are consistent with disc accretion.