We study the magnetoconductivity induced by the axial anomaly via the chiral magnetic effect in strongly coupled holographic models. An important ingredient in our models is that the axial charge is non-conserved beyond the axial anomaly. We achieve this either by explicit symmetry breaking via a non-vanishing non-normalisable mode of an axially charged scalar or using a Stückelberg field to make the AdS-bulk gauge field massive. The DC magnetoconductivites can be calculated analytically. They take a universal form in terms of gauge field mass at the horizon and quadratic dependence on the magnetic field. The axial charge relaxation time grows linearly with magnetic field in the large regime. Most strikingly positive magnetoconductivity is still present even when the relaxation times are short and the axial charge can not be thought of as an approximate symmetry. In the explicit breaking model, we also observe that the chiral separation conductivity and the axial magnetic conductivity for the consistent axial current vanish in the limit of strong symmetry breaking.