We study the effect of the external electrostatic field on dipolar fluid mixtures by extending the algebraic perturbation theory of Kalikmanov [Phys. Rev. E 59, 4085 (1999), valid for one-component dipolar fluids] to the multicomponent case. Our reference system is a dipolar hard sphere mixture, while the external field is treated as a perturbation. Using the mean spherical approximation to describe the reference system in the case when the components differ only by their dipole moments (and not their size), the external field contributions to the free energy, pressure and chemical potentials are derived. As an application, we use these expressions to examine the field dependence of the isomerization equilibrium in a two-component dipolar mixture. It is found that in isomerization equilibrium, the concentration of the more dipolar component increases with the external field, as well as the dielectric constant of the mixture, while the pressure is decreased by the field.