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Context. As recently demonstrated, high-z submillimetre galaxies (SMGs) are the perfect background sample for tracing the mass density profiles of galaxies and clusters (baryonic and dark matter) and their time-evolution through gravitational lensing. Their magnification bias, a weak gravitational lensing effect, is a powerful tool for constraining the free parameters of a halo occupation distribution (HOD) model and potentially also some of the main cosmological parameters. Aims. The aim of this work is to test the capability of the magnification bias produced on high-z SMGs as a cosmological probe. We exploit cross-correlation data to constrain not only astrophysical parameters ($M_{min}$, $M_1$, and $α$), but also some of the cosmological ones ($Ω_m$, $σ_8$, and $H_0$) for this proof of concept. Methods. The measured cross-correlation function between a foreground sample of GAMA galaxies with spectroscopic redshifts in the range 0.2 < z < 0.8 and a background sample of H-ATLAS galaxies with photometric redshifts >1.2 is modelled using the traditional halo model description that depends on HOD and cosmological parameters. These parameters are then estimated by performing a Markov chain Monte Carlo analysis using different sets of priors to test the robustness of the results and to study the performance of this novel observable with the current set of data Results. With our current results, $Ω_m$ and $H_0$ cannot be well constrained. However, we can set a lower limit of >0.24 at 95\% confidence level (CL) on $Ω_m$ and we see a slight trend towards $H_0>70$ values. For our constraints on $σ_8$ we obtain only a tentative peak around 0.75, but an interesting upper limit of $σ_8\lesssim 1$ at 95\% CL. We also study the possibility to derive better constraints by imposing more restrictive priors on the astrophysical parameters.