We study the spectrum and the transport properties of two identical, vertically coupled quantum dots in a perpendicular magnetic field. We find correlation-induced energy crossings in a magnetic field sweep between states differing only in the vertical degree of freedom. Considering the influence of a slight asymmetry between the dots caused by the applied source–drain voltage in vertical transport experiments, these crossings convert to anticrossings accompanied by the build-up of charge polarization which is tunable by the perpendicular magnetic field. The polarization strongly affects the vertical transport through the double quantum dot and is manifest in an isospin blockade and the appearance of negative differential conductances in the magnetic field range where the charge localization occurs.