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Accreting supermassive black holes at the centres of active galaxies often produce 'jets'--collimated bipolar outflows of relativistic particles (1).Magnetic fields probably play a critical role in jet formation (2,3) and in accretion disk physics (4). A dynamically important magnetic field was recently found near the Galactic Centre black hole (5). If this is common and if the field continues to near the black hole event horizon, disk structures will be affected, invalidating assumptions made in standard models (3,6,7). Here we report that jet magnetic field and accretion disk luminosity are tightly correlated over seven orders of magnitude for a sample of 76 radio-loud active galaxies. We conclude that the jet-launching regions of these radio-loud galaxies are threaded by dynamically important fields, which will affect the disk properties. These fields obstruct gas infall, compress the accretion disk vertically, slow down the disk rotation by carrying away its angular momentum in an outflow (3) and determine the directionality of jets (8)., General relativistic magnetohydrodynamic simulations find that if the accretion disk is threaded with enough poloidal magnetic flux, the flux will be transported inwards and accumulate in the central region of [...]