Allowing non-matching interfaces in a computational solver offers significant flexibility, and the potential to simplify the mesh generation process and reduce the number of required cells. A universal meshless interpolation method, suitable for data interpolation across non-matching interfaces, is presented here. The method is based on radial basis function volume interpolation and is applicable to data transfer in any computational mechanics solver, in any number of dimensions. Previous work has considered analytical test cases and scalar wave propagation problems, transferring data across non-matching mesh boundaries, and the cost and achievable spatial order of convergence considered. The method is here implemented into a structured multiblock finite-volume flow solver, and implementation issues discussed. Internal and external two-dimensional test cases are considered with discontinuous mesh spacing across block boundaries. A spatial order of convergence study is presented for an aerofoil case, and it is shown that including a discontinuous interface does not affect the solution accuracy or the order of convergence.