The broadening in photoelectron spectra of polymers can be attributed to several factors, such as light source spread, spectrometer resolution, the finite lifetime of the hole state, and solid-state effects. Here, for the first time, we set up a computational protocol to assess the peak broadening induced for both core and valence levels by solid-state effects in four amorphous polymers by using a combination of density functional theory, many-body perturbation theory, and classical polarizable embedding. We show that intrinsic local inhomogeneities in the electrostatic environment induce a Gaussian broadening of 0.2-0.7 eV in the binding energies of both core and semivalence electrons, corresponding to a full width at half-maximum (FWHM) of 0.5-1.7 eV for the investigated systems. The induced broadening is larger in acrylate-based than in styrene-based polymers, revealing the crucial role of polar groups in controlling the roughness of the electrostatic landscape in the solid matrix.