Angular distributions for the elastic scattering of 8Li on 9Be and the neutron transfer reactions 9Be(8Li,7Li)10Be and 9Be(8Li,9Li)8Be have been measured with a 27 MeV 8Li radioactive nuclear beam. Spectroscopic factors for 8Li|n=9Li and 7Li|n=8Li bound systems were obtained from the comparison between the experimental differential cross section and finite-range DWBA calculations with the code FRESCO. The spectroscopic factors obtained are compared to shell model calculations and to other experimental values from (d,p) reactions. Using the present values for the spectroscopic factor, cross sections for the direct neutron-capture reactions 7Li(n,g)8Li and 8Li(n,g)9Li were calculated in the framework of a potential model.