  Motivated by the isotropy of the CMB spectrum, all existing studies of
magnetised cosmological perturbations employ FRW backgrounds. However, it is
important, to know the limits of this approximation and the effects one loses
by neglecting the anisotropy of the background magnetic field. We develop a new
treatment, which fully incorporates the anisotropic magnetic effects by
allowing for a Bianchi I background universe. The anisotropy of the unperturbed
model facilitates the closer study of the coupling between magnetism and
geometry. The latter leads to a curvature stress, which accelerates positively
curved perturbed regions and balances the effect of magnetic pressure gradients
on matter condensations. We argue that the tension carried along the magnetic
force-lines is the reason behind these magneto-curvature effects. For a
relatively weak field, we also compare to the results of the almost-FRW
approach. We find that some of the effects identified by the FRW treatment are
in fact direction dependent, where the key direction is that of the background
magnetic field vector. Nevertheless, the FRW-based approach to magnetised
cosmological perturbations remains an accurate approximation, particularly on
large scales, when one looks at the lowest order magnetic impact on
gravitational collapse. On small scales however, the accuracy of the perturbed
Friedmann framework may be compromised by extra shear effects.
