Understanding the sources responsible for reionizing the Universe is a key goal of observational cosmology. A discrepancy has existed between the meta-galactic hydrogen ionisation rate, $\Gamma_{\rm HI}$, predicted by early hydrodynamical simulations of the Lyman-$\alpha$ forest if scaled to appropriate assumptions for the IGM temperature, when compared to values predicted from the proximity effect. We present new estimates for $\Gamma_{\rm HI}$ in the redshift range $2<z<4$ based on hydrodynamical simulations of the Lyman-$\alpha$ forest opacity. Within the current concordance cosmology, and assuming updated QSO emissivity rates, a substantial contribution to the UV background from young star-forming galaxies appears to be required over the entire redshift range. Our results are consistent with lower-end estimates from the proximity effect. It is also found that the errors on the ionisation rate are dominated by uncertainties in the thermal state of the intergalactic medium and the r.m.s fluctuation amplitude at the Jeans scale.