By means of a three-dimensional full-wave analytical-numerical technique we consider the diffraction of a VLF point source field by a localized perturbation in the lower ionosphere, which is taken as a truncated highly conducting cylinder. The surface impedance concept is additionally used to model the Earth-ionosphere waveguide. Our approach is based on the preliminary asymptotic integration of the rigorous two-dimensional integral equation in order to facilitate its further numerical handling, and an original computational algorithm is proposed to obtain a solution of the approximate equation. By reducing CPU time, the procedure developed enables us to study both small and comparatively large irregularities. The theoretical computations have yielded the following findings: (1) the transverse dimension of the reflecting area, which can explain the experimental result, may be reduced as compared with that suggested before, (2) scattering may be significant not only in the forward direction but also in the backward direction and out-of-the-way directions, and (3) the same ionospheric perturbation produces a noticeably smaller effect on subionospheric VLF radio wave propagation for daytime conditions than for nighttime ones.