Total cross sections are computed for electron capture from the ground states of H and He by fast protons using the Corrected first-Born (CB1) approximation. Particular emphasis is given to the formation of atomic hydrogen in excited states 2s, 2p, 3s, 3p, 3d and 4s for which experimental data are available. Detailed comparisons with the measurements are carried out, with the purpose of assessing the validity and utility of the CB1 method for prediction of state-selective cross sections.