We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. The electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electric fields, the interplay between this tunable band gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele spin-orbit coupling induces a transition from a topological to a band insulator, whereas at much higher electric fields silicene becomes a semimetal.