The WMAP satellite, devoted to observations of the anisotropies of the cosmic microwave background radiation, has recently provided a determination of the baryonic density of the universe with unprecedented precision. Using this, big bang nucleosynthesis calculations predict a primordial Li abundance that is a factor of 2-3 higher than that observed in Galactic halo dwarf stars. It has been argued that this discrepancy could be resolved if the Be(d, p)2α reaction rate were around a factor of 100 larger than has previously been considered. We have now studied this reaction, for the first time at energies appropriate to the big bang environment, at the CYCLONE radioactive-beam facility at Louvain-la-Neuve. The cross section was found to be a factor of 10 smaller than derived from earlier measurements. It is concluded therefore that nuclear uncertainties cannot explain the discrepancy between observed and predicted primordial Li abundances, and an alternative astrophysical solution must be investigated.