The development of a hybrid high order time domain finite element solution procedure for the simulation of two dimensional problems in computational electromagnetics is considered. The chosen application area is that of electromagnetic scattering. The spatial approximation adopted incorporates both a continuous Galerkin spectral element method and a high order discontinuous Galerkin method. Temporal discretisation is achieved by means of a fourth order Runge-Kutta procedure. An exact analytical solution is employed initially to validate the procedure and the numerical performance is then demonstrated for a number of more challenging examples.