The p - p-chain reaction 3He(α, γ)7Be can sensitively influence the prediction of the 7Be and 8B neutrino fluxes. Despite its importance, the knowledge of its reaction cross section at energies of the core of the Sun (15 keV 30 keV) is limited and the accuracy far from the desired 3% level. In the present paper the indirect measurement of the external capture contribution using the asymptotic normalization coefficient (ANC) technique is reported. The angular distributions of deuterons emitted in the 6Li(3He,d)7Be α-transfer reactions were measured and the ANCs extracted from the scaling of distorted-wave Born approximation (DWBA) and coupled-channel (CC) calculations. Then, the astrophysical S-factor for the 3He(α, γ)7Be reaction was calculated assuming E1 direct capture and the zero energy value turned out to be 0.534 0.025 keVb. Both our experimental and theoretical approaches were benchmarked through the analysis of the 6Li(p,γ)7Be astrophysical factor, with interesting astrophysical applications to the understanding of the primordial lithium problem. In particular, the present work disfavors the occurrence of a claimed 200 keV resonance in the astrophysical factor.