We present an accurate method of treating the one-neutron removal reaction at intermediate incident energies induced by both nuclear and Coulomb interactions. In the method, the nuclear and Coulomb breakup processes are consistently treated by the method of continuum discretized coupled channels without making the adiabatic approximation to the Coulomb interaction, so that the removal cross section calculated never diverges. This method is applied to a recently measured one-neutron removal cross section for 31Ne+ 12C scattering at 230 MeV/nucleon and 31Ne+ 208Pb scattering at 234 MeV/nucleon. The spectroscopic factor and asymptotic normalization coefficient of the last neutron in 31Ne are evaluated.
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