We show that the features of the recent astrophysically motivated model by Granato et al. are fully consistent with the available statistical measurements of galaxies at (sub)millimetre wavelengths. We quantitatively predict the impact of this scenario on near-future cosmological observations dealing with spatial and flux statistical distribution of (sub)millimetre galaxies. We show that the expected angular correlation function of spheroids is compatible with available data. We compute the expected power spectrum of fluctuations due to clustering at the frequencies of the High Frequency Instrument (HFI) on ESA's Planck satellite: the clustering signal is found to be detectable in regions of low interstellar dust emission. A further distinctive prediction of the adopted model is a remarkably high fraction of gravitationally lensed sources at bright millimetre/submillimetre fluxes. In fact, since most spheroids burn at redshift z≃ 2–3 according to the adopted model, gravitational lensing amplifies a significant number of high-z forming spheroidal galaxies, which will be detectable by large-area, shallow surveys at millimetre/submillimetre wavelengths, such as those carried out by Planck/HFI. Allowing for other source populations, we find that the fraction of gravitationally lensed millimetre/submillimetre sources at fluxes >100 mJy is expected to be up to ≃40 per cent.