A modelling technique is proposed for direct use of the discrete complex image method (DCIM) to derive closed-form expressions for electric field components encountered in the electric field integral equation (EFIE) representing a lossy half space problem. The technique circumvents time consuming numerical computation of Sommerfeld integrals by approximating the kernel of the integrals with appropriate mathematical functions. This is done by appropriate use of either the least-square Prony (LS-Prony) method or the matrix pencil method (MPM) to represent electric field expressions in terms of spherical waves and their derivatives. A comparison is made between the two methods based on the computation time and accuracy and it is shown that the LS-Prony method performs two-three times faster than the MPM in approximating the integral kernels depending on the platform. The main feature of the proposed technique is its ability for direct inclusion in the kernel of computational tools based on the method of moments solution of the EFIE. This can be viewed as an advantage over the conventional DCIM approximation of spatial Green's functions for mixed potential integral equation for cases where the problem in hand can be more efficiently represented by the EFIE (e.g. the thin-wire EFIE). The accuracy of the proposed technique is validated against numerical integration of Sommerfeld integrals for an arbitrary electric dipole inside a lossy half space.