Propagation-based neutron phase-contrast tomography is demonstrated using the ISIS pulsed spallation source. The proof-of-concept tomogram with a Paganin-type phase-retrieval filter applied exhibits an effective net boost of $23\ifmmode\pm\else\textpm\fi{}1$ in the signal-to-noise ratio as compared with an attenuation-based tomogram, implying a boost in the effective degree of neutron brilliance of over 2 orders of magnitude. This comparison is for phase retrieval versus conventional absorption with no additional collimation in place. We provide expressions for the optimal phase-contrast geometry as well as conditions for the validity of the method. The underpinning theory is derived under the assumption of the sample being composed of a single material. The effective boost in brilliance may be employed to give reduced acquisition time, or may instead be used to keep exposure times fixed while improving the measured contrast.