We present a new deep spectroscopic catalogue for Abell 85, within 3.0 × 2.6 Mpc2 and down to Mr ˜ Mr^{ast } +6. Using the Visible Multi-Object Spectrograph at the Very Large Telescope and the AutoFiber 2 at the William Herschel Telescope, we obtained almost 1430 new redshifts for galaxies with mr ≤ 21 mag and <μe,r>≤ 24 mag arcsec-2. These redshifts, together with Sloan Digital Sky Survey Data Release 6 and NASA/IPAC Extragaalctic Database spectroscopic information, result in 460 confirmed cluster members. This data set allows the study of the luminosity function (LF) of the cluster galaxies covering three orders of magnitudes in luminosities. The total and radial LFs are best modelled by a double Schechter function. The normalized LFs show that their bright (Mr ≤ -21.5) and faint (Mr ≥ -18.0) ends are independent of clustercentric distance and similar to the field LFs unlike the intermediate luminosity range (-21.5 ≤ Mr ≤ -18.0). Similar results are found for the LFs of the dominant types of galaxies: red, passive, virialized and early-infall members. On the contrary, the LFs of blue, star forming, non-virialized and recent-infall galaxies are well described by a single Schechter function. These populations contribute to a small fraction of the galaxy density in the innermost cluster region. However, in the outskirts of the cluster, they have similar densities to red, passive, virialized and early-infall members at the LF faint end. These results confirm a clear dependence of the colour and star formation of Abell 85 members in the cluster centric distance.