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 Bi<sub>2</sub>WO<sub>6</sub> and the replacement of W<sup>6+</sup> by pentavalent (Nb<sup>5+</sup>, Ta<sup>5+</sup>) and tetravalent (Ti<sup>4+</sup>, Sn<sup>4+</sup>) ions, with charge neutrality maintained by the formation of a mixed-anion oxyhalide sublattice. We find that Bi<sub>2</sub>SnO<sub>4</sub>F<sub>2</sub> is thermodynamically unstable, in contrast to Bi<sub>2</sub>TaO<sub>5</sub>F, Bi<sub>2</sub>NbO<sub>5</sub>F and Bi<sub>2</sub>TiO<sub>4</sub>F<sub>2</sub>. The electric dipoles introduced by chemical substitutions in the parent compound are found to suppress the spontaneous polarization from 61.55 μC/cm<sup>2</sup> to below 15.50 μC/cm<sup>2</sup>. 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.<br>