The anomaly in lithium abundance is a well-known unresolved problem in nuclear astrophysics. A recent revisit to the problem tried the avenue of resonance enhancement to account for the primordial 7Li abundance in standard big-bang nucleosynthesis. Prior measurements of the 7Be(d,p)8Be∗ reaction could not account for the individual contributions of the different excited states involved, particularly at higher energies close to the Q value of the reaction. We carried out an experiment at HIE-ISOLDE, CERN to study this reaction at Ec.m.=7.8 MeV, populating excitations up to 22 MeV in 8Be for the first time. The angular distributions of the several excited states have been measured and the contributions of the higher excited states in the total cross section at the relevant big-bang energies were obtained by extrapolation to the Gamow window using the talys code. The results show that by including the contribution of the 16.63 MeV state, the maximum value of the total S factor inside the Gamow window comes out to be 167 MeV b as compared to earlier estimate of 100 MeV b. However, this still does not account for the lithium discrepancy.