The silicon-vacancy centre () in diamond has exceptional spectral properties for single-emitter quantum information applications. Most of the fluorescence is concentrated in a strong zero phonon line (ZPL), with a weak phonon sideband extending for 100 nm that contains several clear features. We demonstrate that the ZPL position can be used to reliably identify the silicon isotope present in a single centre. This is of interest for quantum information applications since only the 29Si isotope has nuclear spin. In addition, we show that the sharp 64 meV phonon peak is due to a local vibrational mode of the silicon atom. The presence of a local mode suggests a plausible origin of the measured isotopic shift of the ZPL.