Plasma irregularities in the equatorial E region ionosphere are classified as Type I or Type II, based on coherent radar spectra. Type I irregularities are attributed to the Farley‐Buneman instability and Type II to the gradient drift instability that cascades to meter‐scale irregularities detected by radars. This work presents the first kinetic simulations of coupled Farley‐Buneman and gradient drift turbulence in the equatorial E region ionosphere for a range of zeroth‐order vertical electric fields, using a new approach to solving the electrostatic potential equation. The simulation models a collisional quasi‐neutral plasma with a warm, inertialess electron fluid and a distribution of NO+ ions. A 512 m wave with a maximum/minimum of ±0.25 of the background density perturbs the plasma. The density wave creates an electrostatic field that adds to the zeroth‐order vertical and ambipolar fields, and drives Farley‐Buneman turbulence even when these fields are below the instability threshold. Wave power spectra show that Type II irregularities develop in all simulation runs and that Type I irregularities with wavelengths of a few meters develop in the trough of the background wave in addition to Type II irregularities as the zeroth‐order electric field magnitude increases. Linear fluid theory predicts the growth of Type II irregularities reasonably well, but it does not fully capture the simultaneous growth of Type I irregularities in the region of peak total electric field. The growth of localized Type I irregularities represents a parametric instability in which the electric field of the large‐scale background wave drives pure Farley‐Buneman turbulence. These results help explain observations of meter‐scale irregularities advected by kilometer‐scale waves.