We present a new technique for modelling submillimetre galaxies (SMGs): the 'Count Matching' approach. Using light cones drawn from a semi-analytic model of galaxy formation, we choose physical galaxy properties given by the model as proxies for their submillimetre luminosities, assuming a monotonic relationship. As recent interferometric observations of the Extended Chandra Deep Field-South show that the brightest sources detected by single-dish telescopes are comprised by emission from multiple fainter sources, we assign the submillimetre fluxes so that the combined Large APEX BOlometer CAmera (LABOCA) plus bright-end Atacama Large Millimeter/submillimeter Array observed number counts for this field are reproduced. After turning the model catalogues given by the proxies into submillimetre maps, we perform a source extraction to include the effects of the observational process on the recovered counts and galaxy properties. We find that for all proxies, there are lines of sight giving counts consistent with those derived from LABOCA observations, even for input sources with randomized positions in the simulated map. Comparing the recovered redshift, stellar mass and host halo mass distributions for model SMGs with observational data, we find that the best among the proposed proxies is that in which the submillimetre luminosity increases monotonically with the product between dust mass and star formation rate (SFR). This proxy naturally reproduces a positive trend between SFR and bolometric IR luminosity. The majority of components of blended sources are spatially unassociated.