Microscopic calculations of the electromagnetic response of medium-mass nuclei are now feasible thanks to the availability of realistic nuclear interactions with accurate saturation and spectroscopic properties, and the development of large-scale computing methods for many-body physics. The purpose is to compute isovector dipole electromagnetic (E1) response and related quantities, i.e. integrated dipole cross section and polarizability, and compare with data from photoabsorption and Coulomb excitation experiments. The single-particle propagator is obtained by solving the Dyson equation, where the self-energy includes correlations non-perturbatively through the Algebraic Diagrammatic Construction (ADC) method. The particle-hole ($ph$) polarization propagator is treated in the Dressed Random Phase Approximation (DRPA), based on an effective correlated propagator that includes some $2p2h$ effects but keeps the same computation scaling as the standard Hartree-Fock propagator. The E1 responses for $^{14,16,22,24}$O, $^{36,40,48,52,54,70}$Ca and $^{68}$Ni have been computed: the presence of a soft dipole mode of excitation for neutron-rich nuclei is found, and there is a fair reproduction of the low-energy part of the experimental excitation spectrum. This is reflected in a good agreement with the empirical dipole polarizability values. For a realistic interaction with an accurate reproduction of masses and radii up to medium-mass nuclei, the Self-Consistent Greens Function method provides a good description of the E1 response, especially in the part of the excitation spectrum below the Giant Dipole Resonance. The dipole polarizability is largely independent from the strategy of mapping the dressed propagator to a simplified one that is computationally manageable
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