Theoretical models of galaxy formation based on the cold dark matter cosmogony typically require strong feedback from supernova (SN) explosions in order to reproduce the Milky Way satellite galaxy luminosity function and the faint end of the field galaxy luminosity function. However, too strong a SN feedback also leads to the universe reionizing too late, and the metallicities of Milky Way satellites being too low. The combination of these four observations therefore places tight constraints on SN feedback. We investigate these constraints using the semi-analytical galaxy formation model galform. We find that these observations favour a SN feedback model in which the feedback strength evolves with redshift. We find that, for our best fit model, half of the ionizing photons are emitted by galaxies with rest-frame far-UV absolute magnitudes $M_{\rm AB}(1500{\rm \AA})<-17.5$, which implies that already observed galaxy populations contribute about half of the photons responsible for reionization. The $z=0$ descendants of these galaxies are mainly galaxies with stellar mass $M_*>10^{10}\,{\rm M}_{\odot}$ and preferentially inhabit halos with mass $M_{\rm halo}>10^{13}\,{\rm M}_{\odot}$.