In this paper, a novel Computer Aided Design (CAD) free, mesh-based aerodynamic design optimisation framework is presented. It is demonstrated by optimising the aerodynamic performance of a spaceplane concept, provided by an industrial partner Reaction Engines Ltd (REL), across the transonic and low supersonic regime. The framework makes use of both evolutionary and Bayesian [2] optimisation approaches and this paper presents a comparison of the performance of both optimisation schemes on a range of test cases. The developed framework enables users to define a set of parameterised transformations that act on a subset of target nodes on the computational surface mesh. Radial Basis Function (RBF) mesh morphing is used to ensure the shape of the boundary between target nodes and surrounding nodes is preserved. The natural implementatoin of geometric constraints, such as geometry preservation of user-defined regions, is also demonstrated. The presented approach is demonstrated to reduce the overall time spent by engineers generating surface meshes for new geometries, which in conventional optimisation approaches is a significant bottleneck. The robustness of the mesh morphing approach is demonstrated by applying it to multiple unstructured mesh test cases. Ultimatley the proposed scheme is used to perform an industrial scale design optimisation of a novel spaceplane design concept. It is shown that it was possible to achieve a 1.6% reduction of drag across the transonic Mach regime under volume and lift constraints.