Experiments using the Surface Force Apparatus (SFA) have found anomalously long ranged charge-charge underscreening in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be the possible origin of this behaviour. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric constant, $\varepsilon_r$, is unable to resolve the anomalous underscreening seen in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric constant in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged interactions between charged surfaces at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric constant remains uniform does not display similar clusters, even with $\varepsilon_r$ equal to the saturated value at ion contact. Hence, the observed behaviours are not simply due to an enhanced Coulomb interaction.
