The origin of strong ( > ∼ 1𝑀𝐺) magnetic fields in white dwarfs has been a puzzle for decades. Recently, a dynamo mechanism operating in rapidly rotating and crystallizing white dwarfs has been suggested to explain the occurrence rates of strong magnetic fields in white dwarfs with close low-mass main sequence star companions. Here we investigate whether the same mechanism may produce strong magnetic fields in close double white dwarfs. The only known strongly magnetic white dwarf that is part of a close double white dwarf system, the magnetic component of NLTT 12758, is rapidly rotating and likely crystallizing and therefore the proposed dynamo mechanism represents an excellent scenario for the origin of its magnetic field. Presenting a revised formation scenario for NLTT 12758, we find a natural explanation for the rapid rotation of the magnetic component. We furthermore show that it is not surprising that strong magnetic fields have not been detected in all other known double white dwarfs. We therefore conclude that the incidence of magnetic fields in close double white dwarfs supports the idea that a rotation and crystallization driven dynamo plays a major role in the generation of strong magnetic fields in white dwarfs.