We study how the magnetic field dependence of the Eck step voltage in long Josephson tunnel junctions (LJTJs) can allow for ultra-low-noise magnetic sensing. The field to be measured is applied perpendicular to a continuous superconducting pickup loop. Wherever the loop has a narrow constriction, the density of the flux-restoring circulating currents will become relatively high and will locally create a magnetic field large enough to bring a biased LJTJ into the flux-flow state, ie, at a finite voltage proportional to the field strength. This method allows the realization of a novel family of robust and general-purpose superconducting devices which, despite their simplicity, function as ultra-low-noise, wide-band and high-dynamics magnetometers. The performance of low-T c sensor prototypes, including a highly linear voltage responsivity and an intrinsic voltage spectral density in the pV Hz− 1/2 range, promises to …