ABSTRACT Rings and gaps are commonly observed in the dust continuum emission of young stellar discs. Previous studies have shown that substructures naturally develop in the weakly ionized gas of magnetized, non-ideal MHD discs. The gas rings are expected to trap large mm/cm-sized grains through pressure gradient-induced radial dust–gas drift. Using 2D (axisymmetric) MHD simulations that include ambipolar diffusion and dust grains of three representative sizes (1 mm, 3.3 mm, and 1 cm), we show that the grains indeed tend to drift radially relative to the gas towards the centres of the gas rings, at speeds much higher than in a smooth disc because of steeper pressure gradients. However, their spatial distribution is primarily controlled by meridional gas motions, which are typically much faster than the dust–gas drift. In particular, the grains that have settled near the mid-plane are carried rapidly inwards by a fast accretion stream to the inner edges of the gas rings, where they are lifted up by the gas flows diverted away from the mid-plane by a strong poloidal magnetic field. The flow pattern in our simulation provides an attractive explanation for the meridional flows recently inferred in HD 163296 and other discs, including both ‘collapsing’ regions where the gas near the disc surface converges towards the mid-plane and a disc wind. Our study highlights the prevalence of the potentially observable meridional flows associated with the gas substructure formation in non-ideal MHD discs and their crucial role in generating rings and gaps in dust.