Abstract We investigated a cosmological model that allows a momentum transfer between dark matter and dark energy. The interaction in the dark sector mainly affects the behaviour of perturbations on small scales while the background evolution matches the w CDM solution. As a result of the momentum transfer, these kinds of models help alleviating the σ 8 discrepancy in the standard model, but do not resolve the so-called H 0 tension. We confirm that this is indeed the case by computing cosmological constraints. While our analysis tends to favour σ 8 values lower than in ΛCDM, we do not find evidence for a non-vanishing momentum transfer in the dark sector. Since upcoming galaxy surveys will deliver information on scales and red-shift relevant for testing models allowing momentum transfer in the dark sector, we also carried out forecasts using different survey configurations. We assessed the relevance of neglecting lensing convergence κ when modelling the angular power spectrum of number counts fluctuations C ℓ ij ( z,z' ). We found that not including κ in analyses leads to biased constraints (≈ 1-5 σ ) of cosmological parameters even when including information from other experiments. Incorrectly modelling C ℓ ij ( z,z' ) might lead to spurious detection of neutrino masses and exacerbate discrepancies in H 0 and σ 8 .