  We investigate the radio properties of a sample of 53 sources selected at 850
$\mu$m from the SCUBA-2 Cosmology Legacy Survey using new deep, low-frequency
radio imaging of the Lockman Hole field from the Low Frequency Array. Combining
these data with additional radio observations from the GMRT and the JVLA, we
find a variety of radio spectral shapes and luminosities within our sample
despite their similarly bright submillimetre flux densities. We characterise
their spectral shapes in terms of multi-band radio spectral indices. Finding
strong spectral flattening at low frequencies in ~20% of sources, we
investigate the differences between sources with extremely flat low-frequency
spectra and those with `normal' radio spectral indices. As there are no other
statistically significant differences between the two subgroups of our sample
as split by the radio spectral index, we suggest that any differences are
undetectable in galaxy-averaged properties that we can observe with our
unresolved images, and likely relate to galaxy properties that we cannot
resolve, on scales $\lesssim$ 1 kpc. We attribute the observed spectral
flattening in the radio to free-free absorption, proposing that those sources
with significant low-frequency spectral flattening have a clumpy distribution
of star-forming gas. We estimate an average spatial extent of absorbing
material of at most several hundred parsecs to produce the levels of absorption
observed in the radio spectra. This estimate is consistent with the
highest-resolution observations of submillimetre galaxies in the literature,
which find examples of non-uniform dust distributions on scales of ~100 pc,
with evidence for clumps and knots in the interstellar medium. Additionally, we
find two bright (> 6 mJy) submm sources undetected at all other wavelengths. We
speculate that these objects may be very high redshift sources, likely residing
at z > 4.
