If the dark matter haloes of galaxies contain large numbers of subhaloes as predicted by the Lambda cold dark matter model, these subhaloes are expected to appear in strong galaxy-galaxy lens systems as small-scale perturbations in individual images. We simulate observations of multiply lensed sub-mm galaxies at z similar to 2 as a probe of the dark matter halo of a lens galaxy at z similar to 0.5. We present detection limits for dark substructures based on a visibility plane analysis of simulated Atacama Large Millimeter/submillimeter Array (ALMA) data in bands 7, 8 and 9. We explore two effects: local surface brightness anomalies on angular scales similar to the Einstein radius and the astrometric shift of macroimages. This improves the sensitivity of our lens modelling to the mass of the lens perturber. We investigate the sensitivity of the detection of low-mass subhaloes to the projected position of the subhalo on the image plane as well as the source structure and inner density profile of the lens. We demonstrate that, using the most extended ALMA configuration, pseudo-Jaffe subhaloes can be detected with 99 per cent confidence down to M = 10(7)M(circle dot) . We show how the detection threshold for the three ALMA bands depends on the projected position of the subhalo with respect to the lensed images and conclude that, despite the highest nominal angular resolution, band 9 provides the poorest sensitivity due to observational noise. All simulations use the ALMA Full ops most extended ALMA configuration setup in CASA.