The compound nuclei 58 Co* and 61 Ni* have been populated at overlapping excitation energies by transfer reactions 56 Fe( 6 Li,α) 58 Co * (surrogate of n+ 57 Co) at E lab = 35.9 MeV and 59 Co( 6 Li,α) 61 Ni * (surrogate of n+ 60 Ni) at E lab = 40.5 MeV respectively. The 57 Co(n,xp) cross sections in the equivalent neutron energy range of 8.6 -18.8 MeV have been determined within the framework of surrogate reaction ratio method using 60 Ni(n,xp) cross section values from the literature as reference. The proton decay probabilities of the compound systems have been determined by measuring evaporated protons at backward angles in coincidence with projectile-like fragments detected around the grazing angle. The measured 57 Co(n,xp) cross sections are in good agreement with both the predictions of talys-1.8 statistical model code with default parameters using different microscopic level densities and data evaluation library jeff-3.3 up to equivalent neutron energy ≈ 12.6 MeV, while for higher energies the measured 57 Co(n,xp) cross sections are found to be consistently higher than the predictions. However, the talys-1.8 calculations with modified values of input potential parameters provide a reasonable reproduction of the measured 57 Co(n,xp) cross sections for the entire neutron energy range. The observed discrepancies at higher energies between the experimental data and the predictions of both the jeff-3.3 library and the talys-1.8 calculations with default parameters indicate the need of new evaluations for this reaction.