The hybrid finite element-boundary integral-uniform geometrical theory of diffraction method with acceleration by the multi-level fast multi-pole method is extended in a way that allows the application of the hybrid method to problems, where the finite element-boundary integral-multi-level fast multi-pole method parts of the model can be directly connected to uniform geometrical theory of diffraction regions. This becomes possible by an appropriate utilization of Huygens' principle, together with the fact that the regions exterior to the introduced Huygens surface is free of any fields and can thus be filled with arbitrary materials. As such, the appropriate materials are chosen in order to obtain simple enough bodies, which can be treated by the uniform geometrical theory of diffraction. Since some of the boundary integral basis functions typically touch flat parts of these bodies, the image principle is employed for the accurate evaluation of the corresponding boundary integrals. Numerical results for radiation and scattering problems are presented and compared to reference numerical data. The obtained results prove the feasibility of the procedure and considerable computation time and memory savings.