We use time-resolved photoluminescence from single InP nanowires containing both wurtzite (WZ) and zincblende (ZB) crystalline phases to measure the carrier dynamics of quantum confined excitons in a type-II homostructure. The observed recombination lifetime increases by nearly 2 orders of magnitude from 170 ps for excitons above the conduction and valence band barriers to more than 8400 ps for electrons and holes that are strongly confined in quantum wells defined by monolayer-scale ZB sections in a predominantly WZ nanowire. A simple computational model, guided by detailed high-resolution transmission electron microscopy measurements from a single nanowire, demonstrates that the dynamics are consistent with the calculated distribution of confined states for the electrons and holes.