Photoionization cross sections calculations on the halogen-like ions; Kr$^+$ and Xe$^+$ have been performed for a photon energy range from each ion threshold to 15 eV, using large-scale close-coupling calculations within the Dirac-Coulomb R-matrix approximation. The results from our theoretical work are compared with recent measurements made at the ASTRID merged-beam set-up at the University of Aarhus in Denmark and from the Fourier transform ion cyclotron resonance (FT-ICR) trap method at the SOLEIL synchrotron radiation facility in Saint-Aubin, France and the Advanced Light Soure (ALS). For each of these complex ions our theoretical cross section results over the photon energy range investigated are seen to be in excellent agreement with experiment. Resonance energy positions and quantum defects of the prominent Rydberg resonances series identified in the spectra are compared with experiment for these complex halogen like-ions.