We use the wide-field capabilities of the 2 degree field fibre positioner and the AAOmega spectrograph on the Anglo-Australian Telescope (AAT) to obtain redshifts of galaxies that hosted supernovae during the first 3 years of the Supernova Legacy Survey (SNLS). With exposure times ranging from 10 to 60 ks per galaxy, we were able to obtain redshifts for 400 host galaxies in two SNLS fields, thereby substantially increasing the total number of SNLS supernovae with host galaxy redshifts. The median redshift of the galaxies in our sample that hosted photometrically classified Type Ia supernovae (SNe Ia) is z similar to 0.77, which is 25% higher than the median redshift of spectroscopically confirmed SNe Ia in the 3-year sample of the SNLS. Our results demonstrate that one can use wide-field fibre-fed multi-object spectrographs on 4-m telescopes to efficiently obtain redshifts for large numbers of supernova host galaxies over the large areas of the sky that will be covered by future high-redshift supernova surveys, such as the Dark Energy Survey.