Theoretical uncertainties on non-linear scales are among the main obstacles to exploit the sensitivity of forthcoming galaxy and hydrogen surveys like Euclid or the Square Kilometre Array (SKA). Here, we devise a new method to model the theoretical error that goes beyond the usual cut-off on small scales. The advantage of this more efficient implementation of the non-linear uncertainties is tested through a Markov-Chain-Monte-Carlo (MCMC) forecast of the sensitivity of Euclid and SKA to the parameters of the standard ΛCDM model, including massive neutrinos with total mass Mν, and to 3 extended scenarios, including 1) additional relativistic degrees of freedom (ΛCDM + Mν + Neff), 2) a deviation from the cosmological constant (ΛCDM + Mν + w0), and 3) a time-varying dark energy equation of state parameter (ΛCDM + Mν + (w0,wa )). We compare the sensitivity of 14 different combinations of cosmological probes and experimental configurations. For Euclid combined with Planck, assuming a plain cosmological constant, our method gives robust predictions for a high sensitivity to the primordial spectral index ns (σ(ns)=0.00085), the Hubble constant H0 (σ(H0)=0.141 km/s/Mpc), the total neutrino mass Mν (σ(Mν)=0.020 eV). Assuming dynamical dark energy we get σ(Mν)=0.030 eV for the mass and (σ(w0), σ(wa)) = (0.0214, 0.071) for the equation of state parameters. The predicted sensitivity to Mν is mostly stable against the extensions of the cosmological model considered here. Interestingly, a significant improvement of the constraints on the extended model parameters is also obtained when combining Euclid with a low redshift HI intensity mapping survey by SKA1, demonstrating the importance of the synergy of Euclid and SKA.