The crystal structures of the Aurivillius phase ferroelectrics Bi4Ti3O12, BaBi4Ti4O15 and Ba2Bi4Ti5O18, containing perovskite-like layers consisting of three, four and five adjacent TiO6 octahedra, respectively, have been analysed using high-resolution powder neutron diffraction data. At 2K the structure of Bi4Ti3O12 can be successfully modelled in the orthorhombic space group B2cb, with no evidence of the monoclinic distortion in the ferroelectric phase suggested by previous single crystal studies. At 298K BaBi4Ti4O15 shows a subtle orthorhombic distortion, but without the octahedral tilting seen in related ferroelectric phases, and is refined in space group F2mm. At 298 K Ba2Bi4Ti5O18 adopts a tetragonal polar phase (I4mm), thus displaying a third type of polar distortion within this family. It is suggested that these differences arise from a ‘tolerance factor’ type mechanism whereby the increasing content of the large Ba2+ cation causes a shift from underbonding at the perovskite A-site to underbonding at the perovskite B-site resulting in a change in the mechanism of ferroelectricity from A-site displacements to B-site displacements, akin to the mechanism in BaTiO3.