The Aurivillius phases of complex bismuth oxides have attracted considerable attention due to their lattice polarization (ferroelectricity) and photocatalytic activity. We report a first-principles exploration of Bi2WO6 and the replacement of W6+ by pentavalent (Nb5+, Ta5+) and tetravalent (Ti4+, Sn4+) ions, with charge neutrality maintained by the formation of a mixed-anion oxyhalide sublattice. We find that Bi2SnO4F2 is thermodynamically unstable, in contrast to Bi2TaO5F, Bi2NbO5F and Bi2TiO4F2. The electric dipoles introduced by chemical substitutions in the parent compound are found to suppress the spontaneous polarization from 61.55 μC/cm2 to below 15.50 μC/cm2. Analysis of the trends in electronic structure, surface structure, and ionization potentials are reported. This family of materials can be further extended with control of layer thicknesses and choice of compensating halide species.