The Durham GALFORM semi-analytical galaxy formation model has been shown to reproduce the observed rest-frame 1500Å luminosity function of galaxies well over the whole redshift range z = 5 - 10 . We show that in this model , this galaxy population also emits enough ionizing photons to reionize the Universe by redshift z = 10 , assuming a modest escape fraction of 20 per cent . The bulk of the ionizing photons is produced in faint galaxies during starbursts triggered by galaxy mergers . The bursts introduce a dispersion up to \sim 5 dex in galaxy ionizing luminosity at a given halo mass . Almost 90 per cent of the ionizing photons emitted at z = 10 are from galaxies below the current observational detection limit at that redshift . Photo-ionization suppression of star formation in these galaxies is unlikely to affect this conclusion significantly , because the gas that fuels the starbursts has already cooled out of their host halos . The galaxies that dominate the ionizing emissivity at z = 10 are faint , with M _ { 1500 , { AB } } \sim - 16 , have low star formation rates , \dot { M } _ { \star } \sim 0.06 h ^ { -1 } M _ { \odot } yr ^ { -1 } , and reside in halos of mass M \sim 10 ^ { 9 } h ^ { -1 } M _ { \odot } .