In the vast majority of plasmas produced in the JET tokamak the X-ray emission at energies above about 1keV is dominated by Bremsstrahlung radiation from the background deuterium ions, and both Bremsstrahlung and recombination radiation from one or two light impurity species such as beryllium and carbon. Under these circumstances local values of impurity densities and concentrations, or alternatively of the effective charge Zeff of the ion mixture, are derived from tomographic measurements of the local X-ray emissivity at energies above 1-3keV, in conjunction with measurements of electron density and temperature profiles. These calculations are performed using the intrinsic emissivities due to the impurity ions. The emissivities into the relevant energy bands, determined by the detector and filter characteristics, were calculated assuming coronal ionisation equilibrium, and tabulated as a function of electron temperature. This method offers a good spatial and temporal resolution, and is succesfully applied to most plasma conditions where the relative proportions of impurities are known. We also present a detailed sensitivity study to assess the effects of errors in the input data, and a comparison with established methods based on visible Bremsstrahlung measurements, and charge exchange spectroscopy.