In order to investigate the optical properties of wurtzite (Wz) InP nanowires grown on Si(001) by solid source molecular beam epitaxy with the vapour-liquid-solid method, the growth temperature and V/III pressure ratio have been optimized to remove any zinc-blende insertion. These pure Wz InP nanowires have been investigated by photoluminescence (PL), time-resolved PL and PL excitation. Direct observation of the second and third valence band in Wz InP nanowires using PL spectroscopy at high excitation power have been reported and, from these measurements, a crystal field splitting of 74 meV and a spin-orbit interaction energy of 145 meV were extracted. Based on the study of temperature-dependent optical properties, we have performed an investigation of the thermal escape processes of carriers and the electron-phonon coupling strength.