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.
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