Sanidine crystals from two tuff layers at the base of the Palaeocene Eigg Lava Formation on the Isle of Muck, Inner Hebrides, yield step-wise Ar release plateau ages of 62.8 ± 0.6 (2 σ) and 62.4 ±0.6 Ma using the laser 40Ar/39Ar dating technique. These determinations, which are in accord with, but significantly more precise than earlier results, provide a definitive age for the inception of igneous activity in the Small Isles. From stratigraphical inferences, the Muck ages provide precise, maximum constraints on the possible age of Skye magmatism and possibly most of the British Tertiary Volcanic Province. The new ages significantly predate the oldest ages determined so far for Tertiary magmatism in NE Greenland but are similar to ages obtained from W Greenland and offshore SE Greenland and support the concept that the initiation of regional volcanism was primarily controlled by lithospheric thin spots. The Muck sanidine age appears to precisely date the first manifestation of the impingement of the Iceland mantle plume on the lithosphere beneath NW Scotland.