We present a detailed determination of the restframe B-band galaxy luminosity function (LF) as a function of redshift and star formation activity from z=0 to z=0.75. The dataset used for this purpose is a combined sample of over 1700 redshifts spanning a wide range in apparent magnitude, 11.5<B<24.0, which we term the Autofib Redshift Survey. The sample includes various earlier magnitude-limited surveys constructed by our team as well as a new survey of 1026 redshifts measured for galaxies at intermediate magnitudes. The large range in apparent magnitude sampled allows us to investigate both the nature of the LF at low redshift (z<0.1) and possible evolution in its shape to z=0.75. We find that earlier bright surveys have underestimated the absolute normalisation of the LF. Because the shape of the local LF does not change with the survey apparent magnitude limit, it seems unlikely that the local deficiency arises from an underestimated population of low luminosity galaxies. Furthermore, surface brightness losses cannot be significant unless they conspire to retain the LF shape over a variety of detection thresholds. Our data directly demonstrates that the B-band LF evolves with redshift. This evolution is best represented as a steepening of the faint-end slope of the LF, from alpha=-1.1 at low redshift to alpha=-1.5 at z=0.5. Using [OII] emission as an indicator of star formation activity, we show that the LF of quiescent galaxies has remained largely unchanged since z=0.5, whereas the luminosity density of star-forming galaxies has declined by nearly a factor of 2. The steepening of the overall LF with lookback time is a direct consequence of the increasing space density of blue star-forming galaxies at moderate redshifts.