This thesis presents beyond the standard (BSM) model kaon mixing results calculated on the lattice with simulations at the physical light quark mass. These results were calculated using RBC-UKQCD 2+1 flavour domain wall fermion simulations at the iso-spin symmetric limit, with pion masses ranging from the physical value up to 430 MeV. This thesis presents the bare results of BSM kaon mixing bag parameters and ratios, alongside strange and light meson masses and decay constants, it then details the renormalisation procedure and chiral continuum extrapolation. Finally the renormalised continuum physical point results of beyond the standard model bag parameters, ratio parameters and matrix elements and the standard model bag parameter are presented. The beyond the standard model kaon mixing matrix elements will improve upon previous calculations' precision, and these results will help address previous tensions seen in some of the BSM matrix elements. These quantities are important in the search for new physics.