Dust emission at submillimetre wavelengths allows us to trace the early phases of star formation in the Universe. In order to understand the physical processes involved in this mode of star formation, it is essential to gain knowledge about the dark matter structures - most importantly their masses - that submillimetre galaxies live in. Here we use the magnification effect of gravitational lensing to determine the average mass and dust content of submillimetre galaxies with 250 μm flux densities of S250 > 15 mJy selected using data from the Herschel Multi-tiered Extragalactic Survey. The positions of hundreds of submillimetre foreground lenses are cross-correlated with the positions of background Lyman-break galaxies at z ˜ 3-5 selected using optical data from the Canada-France-Hawaii Telescope Legacy Survey. We detect a cross-correlation signal at the 7σ level over a sky area of 1 deg2, with ˜80 per cent of this signal being due to magnification, whereas the remaining ˜20 per cent comes from dust extinction. Adopting some simple assumptions for the dark matter and dust profiles and the redshift distribution enables us to estimate the average mass of the haloes hosting the submillimetre galaxies to be log 10[M200/M&sun;] = 13.17+ 0.05- 0.08(stat.) and their average dust mass fraction (at radii of >10 kpc) to be Mdust/M200 ≈ 6 × 10-5. This supports the picture that submillimetre galaxies are dusty, forming stars at a high rate, reside in massive group-sized haloes and are a crucial phase in the assembly and evolution of structure in the Universe.