Muon spin relaxation ( mu SR) experiments were carried out in zero field on polycrystalline samples of Hf₂Co and Hf₂CoH₃. In the unhydrided alloy the muon preferentially occupies octahedral interstices and diffuses through a tunnelling mechanism within the network made of adjacent octahedra above 220 K. In contrast, the muon occupies tetrahedral interstices in the hydrided alloy. Muon diffusion takes place through two distinct phonon-assisted tunnelling mechanisms with a possible contribution of overbarrier hopping above 250 K and appears to be strongly enhanced hy the presence of hydrogen. This effect is attributed to the different pathways taken by the muon in hydrided and unhydrided Hf₂Co. A comparison with the hydrogen jump rate measured by perturbed angular correlation in the same hydride provides confirmation that the hydrogen mobility is indeed faster than that of the muon, which appears to be a quite general result in concentrated metallic hydrides.