  Placing bright sub-millimetre galaxies (SMGs) within the broader context of
galaxy formation and evolution requires accurate measurements of their
clustering, which can constrain the masses of their host dark matter halos.
Recent work has shown that the clustering measurements of these galaxies may be
affected by a `blending bias,' which results in the angular correlation
function of the sources extracted from single-dish imaging surveys being
boosted relative to that of the underlying galaxies. This is due to confusion
introduced by the coarse angular resolution of the single-dish telescope and
could lead to the inferred halo masses being significantly overestimated. We
investigate the extent to which this bias affects the measurement of the
correlation function of SMGs when it is derived via a cross-correlation with a
more abundant galaxy population. We find that the blending bias is essentially
the same as in the auto-correlation case and conclude that the best way to
reduce its effects is to calculate the angular correlation function using SMGs
in narrow redshift bins. Blending bias causes the inferred host halo masses of
the SMGs to be overestimated by a factor of $\sim6$ when a redshift interval of
$\delta z=3$ is used. However, this reduces to a factor of $\sim2$ for $\delta
z=0.5$. The broadening of photometric redshift probability distributions with
increasing redshift can therefore impart a mild halo `downsizing' effect onto
the inferred host halo masses, though this trend is not as strong as seen in
recent observational studies.
