The application of high pressure allows control over the unit cell and interatomic spacing of materials without any need for new growth methods or processing while accessing their materials properties in situ. Under these extreme pressures, materials may assume new structural phases and reveal novel properties. Here, unusual phase transition and band renormalization effects in 2D van der Waals Ruddlesden-Popper hybrid lead halide perovskites, which have shown extraordinary optical properties and immense potential in light emission and conversion technologies, are reported. The results show that (CH3 (CH2 )3 NH3 )2 (CH3 NH3 )Pb2 Br7 (n = 2) layers undergo two distinct phase transitions related to PbBr6 octahedra, butylammonium (BA), and methylammonium (MA) molecule tilting motion that leads to rather unique/anomalous bandgap variation with pressure. In contrast, (CH3 (CH2 )3 NH3 )PbBr4 (n = 1) lacks MA molecules and possesses only one pressure-induced phase transition related to PbBr6 octahedra and BA tilting. In this range, the bandgap reduces monotonically, much similar to other inorganic semiconductors and display surprisingly large redshift from 3 to 2.4 eV. Together with theoretical calculations, this study offers unique insights into these pressure-induced changes and extends the understanding of these highly anisotropic layered soft organic perovskite materials under extreme conditions.