We report the results of 870{mu}m continuum observations, using the Large APEX Bolometer Camera, towards 77 class-II, 6.7-GHz methanol masers identified by the Methanol MultiBeam (MMB) survey to map the thermal emission from cool dust towards these objects. These data complement a study of 630 methanol masers associated with compact dense clumps identified from the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) survey. Compact dust emission is detected towards 70 sources, which implies a dust-association rate of 99 per cent for the full MMB catalogue. Evaluation of the derived dust and maser properties leads us to conclude that the combined sample represents a single population tracing the same phenomenon. We find median clump masses of a few 10^3^M_{sun}_ and that all but a handful of sources satisfy the mass-size criterion required for massive star formation. This study provides the strongest evidence of the almost ubiquitous association of methanol masers with massive, star-forming clumps. The fraction of methanol-maser associated clumps is a factor of ~2 lower in the outer Galaxy than the inner Galaxy, possibly a result of the lower metallicity environment of the former. We find no difference in the clump-mass and maser-luminosity distributions of the inner and outer Galaxy. The maser-pumping and clump formation mechanisms are therefore likely to be relatively invariant to Galactic location. Finally, we use the ratio of maser luminosity and clump mass to investigate the hypothesis that the maser luminosity is a good indicator of the evolutionary stage of the embedded source, however, we find no evidence to support this.