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ABSTRACT We present cosmological parameter constraints based on a joint modelling of galaxy–lensing cross-correlations and galaxy clustering measurements in the SDSS, marginalizing over small-scale modelling uncertainties using mock galaxy catalogues, without explicit modelling of galaxy bias. We show that our modelling method is robust to the impact of different choices for how galaxies occupy dark matter haloes and to the impact of baryonic physics (at the $$\sim 2{{\ \rm per\ cent}}$$ level in cosmological parameters) and test for the impact of covariance on the likelihood analysis and of the survey window function on the theory computations. Applying our results to the measurements using galaxy samples from BOSS and lensing measurements using shear from SDSS galaxies and CMB lensing from Planck, with conservative scale cuts, we obtain $$S_8\equiv \left(\frac{\sigma _8}{0.8228}\right)^{0.8}\left(\frac{\Omega _\mathrm{ m}}{0.307}\right)^{0.6}=0.85\pm 0.05$$ (stat.) using LOWZ × SDSS galaxy lensing, and S8 = 0.91 ± 0.1 (stat.) using combination of LOWZ and CMASS × Planck CMB lensing. We estimate the systematic uncertainty in the galaxy–galaxy lensing measurements to be $$\sim 6{{\ \rm per\ cent}}$$ (dominated by photometric redshift uncertainties) and in the galaxy–CMB lensing measurements to be $$\sim 3{{\ \rm per\ cent}}$$, from small-scale modelling uncertainties including baryonic physics.