Data set to accompany the article "Accurate Benchmark Polarizability Tensor Characterisations of Small Conducting Inclusions". Abstract: The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in geological imaging using electrical resistivity tomography. It is known that such objects can be characterised by a Póyla-Szegö (polarizability) tensor. Such characterisations have attracted interest as they can provide object features in a machine learning (ML) classification algorithm and provide an alternative imaging solution. However, to be able train ML algorithms, large dictionaries are required and it is essential that the characterisations are accurate. In this work, we obtain accurate numerical approximations to the tensor coefficients, by applying an adaptive boundary element method. The goal being to provide a sequence of benchmark solutions for the tensor coefficients to allow other software developers check the accuracy of their codes.