Laser-plasma acceleration of protons offers a compact, ultra-fast alternative to conventional acceleration techniques, and is being widely pursued for potential applications in medicine, industry and fundamental science. Creating a stable, collimated beam of protons at high repetition rates presents a key challenge. Here, we demonstrate the generation of multi-MeV proton beams from a fast-replenishing ambient-temperature liquid sheet. The beam has an unprecedentedly low divergence of 1° (≤20 mrad), resulting from magnetic self-guiding of the proton beam during propagation through a low density vapour. The proton beams, generated at a repetition rate of 5 Hz using only 190 mJ of laser energy, exhibit a hundred-fold increase in flux compared to beams from a solid target. Coupled with the high shot-to-shot stability of this source, this represents a crucial step towards applications.