  Using the 870-$\mu$m APEX Telescope Large Area Survey of the Galaxy
(ATLASGAL), we have identified 577 submillimetre continuum sources with masers
from the methanol multibeam (MMB) survey in the region $280\degr < \ell <
20\degr$; $|\,b\,| < 1.5\degr$. 94\,per\,cent of methanol masers in the region
are associated with sub-millimetre dust emission. We estimate masses for ~450
maser-associated sources and find that methanol masers are preferentially
associated with massive clumps. These clumps are centrally condensed, with
envelope structures that appear to be scale-free, the mean maser position being
offset from the peak column density by 0.0 \pm 4". Assuming a Kroupa initial
mass function and a star-formation efficiency of ~30\,per\,cent, we find that
over two thirds of the clumps are likely to form clusters with masses
>20\,\msun. Furthermore, almost all clumps satisfy the empirical mass-size
criterion for massive star formation. Bolometric luminosities taken from the
literature for ~100 clumps range between ~100 and 10$^6$\,\lsun. This confirms
the link between methanol masers and massive young stars for 90\,per\,cent of
our sample. The Galactic distribution of sources suggests that the
star-formation efficiency is significantly reduced in the Galactic-centre
region, compared to the rest of the survey area, where it is broadly constant,
and shows a significant drop in the massive star-formation rate density in the
outer Galaxy. We find no enhancement in source counts towards the southern
Scutum-Centaurus arm tangent at $\ell ~ 315\degr$, which suggests that this arm
is not actively forming stars.
