A current paradigm is that imposing a magnetic field on a turbulent flow damps turbulent fluctuations, on the basis that the motion of electrically conducting fluids in magnetic fields induces Joule dissipation. Nevertheless, magnetic fields promote sufficient scale-dependent anisotropy to profoundly reorganise the structure and scale-to-scale energy transfer of turbulence, so their net effect cannot be understood in terms of the additional dissipation only. Here we show that when turbulence is forced, magnetic fields promote large, nearly 2D structures capturing sufficient energy to offset the loss due to Joule dissipation, with the net effect of increasing the intensity of turbulent fluctuations. This change of paradigm potentially carries important consequences for the dynamics of planetary cores and for a wide range of metallurgical and nuclear engineering applications.