In a previous paper liquid-liquid phase separation had been determined for mixtures of dipolar and non-polar two-centre Lennard-Jones molecules of elongation L = 0.505. Here we present isobaric-isothermal molecular dynamics simulation results for mixtures of dipolar with non-polar molecules where either the non-polar component (I) or both components (II) were made polarizable. The proper treatment of many-body inductive interaction effects, especially in mixtures of polarizable non-polar with dipolar components, show that these inductive forces play an essential role in understanding the thermodynamics and phase behaviour of real polar mixtures. The state point was chosen to be T* = 1.539, p* = 5.617 and mu(*2) = 8, where in non-polarizable polar-non-polar mixtures phase separation had been detected previously. Excess Gibbs energies as a function of composition are obtained directly by the lambda-coupling method for mixtures of type I. With increasing polarizability of the nonpolar component the demixing disappears and the excess functions show more symmetrical behaviour. The excess values for Gibbs free energy, enthalpy and volume have been determined directly from the simulation data, and are given as functions of the composition of the dipolar component. For type II mixtures excess volumes show a more symmetrical shape in comparison with type I, although the uncertainties of the simulation results are quite large.