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The \textit{axial} electromagnetic (EM) perturbations of the black hole (BH)solutions in general relativity coupled to nonlinear electrodynamics (NED) werestudied for both electrically and magnetically charged BHs, assuming that theEM perturbations do not alter the spacetime geometry in our preceding paper[Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, theformalism for the \textit{polar} EM perturbations of the BHs in generalrelativity coupled to the NED is presented. We show that the quasinormal modes(QNMs) spectra of polar EM perturbations of the electrically and magneticallycharged BHs in the NED are not isospectral, contrary to the case of thestandard Reissner-Nordstr\"{o}m BHs in the classical linear electrodynamics. Itis shown by the detailed study of QNMs properties in the eikonal approximationthat the EM perturbations can be a powerful tool to confirm that in the NEDlight ray does not follow the null geodesics of the spacetime. By specifyingthe NED model and comparing axial and polar EM perturbations of theelectrically and magnetically charged BHs, it is shown that QNM spectra of theaxial EM perturbations of magnetically (electrically) charged BH and polar EMperturbations of the electrically (magnetically) charged BH are isospectral,i.e., $\omega_{mag}^{ax}\approx\omega_{el}^{pol}$($\omega_{mag}^{pol}\approx\omega_{el}^{ax}$).

Electromagnetic perturbations of black holes in general relativity coupled to nonlinear electrodynamics: Polar perturbations