The physical characterization and the extended crystallographic study of the double perovskite system Pb2Mn0.6Co0.4WO6 indicate an improper ferroelectric contribution to the polarization induced by the magnetic ordering. In the paramagnetic phase, the compound displays a centrosymmetric orthorhombic double perovskite structure with the Pmcn1' symmetry. The structure is strongly distorted by the lead stereoactivity. Magnetization measurements show two magnetic transitions at 188 and 9 K, but the time-of-flight neutron diffraction data provide evidence for a long-range magnetic ordering only below the second transition. Quantitative structure refinements combined with a comprehensive symmetry analysis indicate the Pm'c2(1)' magnetic space group to be the adequate symmetry to describe the structural distortions and spin ordering in the ground state of the system. The symmetry implies a coexistence of a spontaneous ferromagnetic moment and a ferroelectric polarization along the orthogonal b- and c-axes, respectively, in the long-range ordered structure. Macroscopic measurements confirm the presence of the spontaneous polarization also below the first transition at 188 K, where only short-range magnetic correlations are evidenced by diffuse scattering in neutron diffraction.