ABSTRACT We include a fully coupled treatment of metal and dust enrichment into the Delphi semi-analytic model of galaxy formation to explain the dust content of 13 Lyman break galaxies (LBGs) detected by the Atacama Large millimetre Array (ALMA) REBELS Large Program at z ≃ 7. We find that the galaxy dust mass, Md, is regulated by the combination of Type II supernova dust production, astration, shock destruction, and ejection in outflows; grain growth (with a standard time-scale τ0 = 30 Myr) plays a negligible role. The model predicts a dust-to-stellar mass ratio of $\sim 0.07\!-\!0.1{{\ \rm per\ cent}}$ and a UV-to-total star formation rate relation such that log(ψUV) = −0.05 log(ψ)2 + 0.86 log(ψ) − 0.05 (implying that 55–80 per cent of the star formation is obscured) for REBELS galaxies with stellar mass $M_* = 10^{9}\!-\!10^{10} \rm M_\odot$. This relation reconciles the intrinsic UV luminosity of LBGs with their observed luminosity function at z = 7. However, 2 out of the 13 systems show dust-to-stellar mass ratios ($\sim 0.94\!-\!1.1{{\ \rm per\ cent}}$) that are up to 18 times larger than expected from the fiducial relation. Due to the physical coupling between dust and metal enrichment, even decreasing τ0 to very low values (0.3 Myr) only increases the dust-to-stellar mass ratio by a factor of ∼2. Given that grain growth is not a viable explanation for such high observed ratios of the dust-to-stellar mass, we propose alternative solutions.