Hybrid organic–inorganic perovskites (HOIPs) can undergo diverse phase transitions which give rise to desirable properties such as ferroelectricity and piezoelectricity. Hitherto, the origin of their phase transitions is primarily due to the order–disorder of the organic component while other driving forces remain largely unexplored. In this study, the high-pressure structural evolution of a 2D hybrid lead halide perovskite, [(BA)₂PbI₄] (BA = benzylammonium), was investigated which reveals that its orthorhombic to triclinic transition is driven by the cooperative PbI₆ octahedral tilting, distortion and conformational change of the BA amine cation. Density functional theory calculations demonstrate that [PbI₆]⁴⁻ octahedra slightly tilt and distort to result in overall decreased Pb–I bond lengths and Pb–I–Pb angles but increased I–Pb–I angles, while the BA cation slightly rotates towards its benzene ring across the transition. Moreover, the photoluminescence emission exhibits a red-shift along with the decrease in intensity which could be attributed to the contraction of Pb–I bonds and flattening of Pb–I–Pb bond angles under pressure. Our findings demonstrate that the degree of freedom of the inorganic framework also plays a key role in driving the phase transitions of 2D HOIPs, which needs to be taken into account in investigating symmetry-breaking properties of this emerging class of electronic materials.