Measurements of hadron production in p + C interactions at 31 GeV/c are performed using the NA61/SHINE spectrometer at the CERN SPS. The analysis is based on the full set of data collected in 2009 using a graphite target with a thickness of 4 % of a nuclear interaction length. Inelastic and production cross sections as well as spectra of π ± , K ± , p, K⁰ S and Λ are measured with high precision. These measurements are essential for improved calculations of the initial neutrino fluxes in the T2K long-baseline neutrino oscillation experiment in Japan. A comparison of the NA61/SHINE measurements with predictions of several hadroproduction models is presented.