This study is concerned with a two-dimensional (2D) electron–hole (e–h) system in a strong perpendicular magnetic field with special attention devoted to the Rashba spin–orbit coupling (RSOC). The influence of this interaction on the chemical potential of the Bose–Einstein condensed magnetoexcitons and on the ground-state energy of the metallic-type electron–hole liquid (EHL) is investigated in the Hartree–Fock approximation (HFA). The magnetoexciton ground-state energy, and the energy of the single-particle elementary excitations were obtained. We demonstrated that chemical potential is a monotonic function versus the value of the filling factor with negative compressibility, which leads to instability of the Bose–Einstein condensate of magnetoexcitons. The energy per one e–h pair inside the electron–hole droplets (EHD) is found to be situated on the energy scale lower than the value of the chemical potential of the Bose–Einstein condensed magnetoexcitons with wave vector calculated in the HFA.