A dynamo mechanism driven by differential rotation when stars merge has been proposed to explain the presence of strong fields in certain classes of magnetic stars. In the case of the high field magnetic white dwarfs (HFMWDs), the site of the differential rotation has been variously thought to be the common envelope, the hot outer regions of a merged degenerate core or an accretion disc formed by a tidally disrupted companion that is subsequently accreted by a degenerate core. We have shown previously that the observed incidence of magnetism and the mass distribution in HFMWDs are consistent with the hypothesis that they are the result of merging binaries during common envelope evolution. Here we calculate the magnetic field strengths generated by common envelope interactions for synthetic populations using a simple prescription for the generation of fields and find that the observed magnetic field distribution is also consistent with the stellar merging hypothesis. We use the Kolmogorov-Smirnov test to study the correlation between the calculated and the observed field strengths and find that it is consistent for low envelope ejection efficiency. We also suggest that field generation by the plunging of a giant gaseous planet on to a white dwarf may explain why magnetism among cool white dwarfs (including DZ white dwarfs) is higher than among hot white dwarfs. In this picture a super Jupiter residing in the outer regions of the planetary system of the white dwarf is perturbed into a highly eccentric orbit by a close stellar encounter and is later accreted by the white dwarf.