Measurements of sulphur isotopes in presolar grains can help to identify the astrophysical sites in which these grains were formed. A more precise thermonuclear rate of the 33S(p, γ)34Cl reaction is required, however, to assess the diagnostic ability of sulphur isotopic ratios. We have studied the 33S(3He,d)34Cl proton-transfer reaction at 25MeV using a high-resolution quadrupole–dipole–dipole–dipole magnetic spectrograph. Deuteron spectra were measured at ten scattering angles between 10◦and 55◦. Twenty-four levels in 34Cl over Ex=4.6–5.9MeVwere observed, including three levels for the first time. Proton spectroscopic factors were extracted for the first time for levels above the 33S+p threshold, spanning the energy range required for calculations of the thermonuclear 33S(p, γ)34Cl rate in classical nova explosions. We have determined a new 33S(p, γ)34Cl rate using a Monte Carlo method and have performed new hydrodynamic nova simulations to determine the impact on nova nucleosynthesis of remaining nuclear physics uncertainties in the reaction rate. We find that these uncertainties lead to afactor of ≤5variation in the 33S(p, γ)34Cl rate over typical nova peak temperatures, and variation in the ejected nova yields of S–Ca isotopes by ≤20%. In particular, the predicted 32S/33S ratio is 110–130 for the nova model considered, compared to 110–440 with previous rate uncertainties. As recent type II supernova models predict ratios of 130–200, the 32S/33S ratio may be used to distinguish between grains of nova and supernova origin.