We report measurements of the flux-integrated $\bar{\nu}_\mu$ and $\bar{\nu}_\mu+\nu_\mu$ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam, with a mean neutrino energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\mu^\pm$ and no detected charged pion nor proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$ and $\theta_{\mu}200~{\rm MeV}/c$ and $\theta_{\pi}600~{\rm MeV}/c$ and $\theta_{\rm p}