  Motivated by the significant interaction of convection, rotation and magnetic
field in many astrophysical objects, we investigate the interplay between
large-scale flows driven by rotating convection and an imposed magnetic field.
We utilise a simple model in two dimensions comprised of a plane layer that is
rotating about an axis inclined to gravity. It is known that this setup can
result in strong mean flows; we numerically examine the effect of an imposed
horizontal magnetic field on such flows. We show that increasing the field
strength in general suppresses the time-dependent mean flows, but in some cases
it organises them leading to stronger time-averaged flows. Further, we discuss
the effect of the field on the correlations responsible for driving the flows
and the competition between Reynolds and Maxwell stresses. A change in
behaviour is observed when the (fluid and magnetic) Prandtl numbers are
decreased. In the smaller Prandtl number regime, it is shown that significant
mean flows can persist even when the quenching of the overall flow velocity by
the field is relatively strong.
