We have computed dipole strength distributions for nickel and tin isotopes within the Relativistic Quasiparticle Time Blocking Approximation (RQTBA). These calculations provide a good description of data, including the neutron-rich tin isotopes ^130,132Sn. The resulting dipole strengths have been implemented in Hauser-Feshbach calculations of astrophysical neutron capture rates relevant for r-process nucleosynthesis studies. The RQTBA calculations show the presence of enhanced dipole strength at energies around the neutron threshold for neutron rich nuclei. The computed neutron capture rates are sensitive to the fine structure of the low lying dipole strength, which emphasizes the importance of a reliable knowledge of this excitation mode.