A large number of polished stone implements from Palaeolithic to Bronze Age sites of Northern Italy and Southern France are made of high-pressure (HP) metamorphic rocks (eclogite and related rocks), mainly consisting of Na-pyroxene (jadeite to omphacite) from the metamorphic belt of the Western Alps. The standard archaeometric study of prehistoric stone implements follows a procedure that is invasive, expensive and time-consuming. Since Na-pyroxenes may show a large compositional range, a thorough study of the variations affecting the dhkl values, obtained by X-ray diffraction, of three selected reflections as a function of different chemical composition was carried out, in order to determine the chemistry of Na-pyroxene isomorphic mixtures and roughly evaluate their relative amounts. These reflections (\bar221, 310, 002) are sharp, intense and sensitive to the variation of pyroxene chemical composition. Using such dhkl values measured on pyroxenes of known chemistry, a Ca-pyroxene(Di)-jadeite(Jd)-aegirine(Ae) compositional diagram was constructed, from which the composition of an unknown pyroxene can be estimated within an error of about 5%. When the size of the object is relatively small and a flat polished surface is present, the proposed analytical procedure becomes totally non-invasive. The data obtained shed light on the provenance sources of such implements and the prehistoric trade routes.