A high temperature superconducting cable may be based on a centrally located cylindrical support, a so-called former. If electrically conductive, the former can contribute to the AC losses through eddy current losses caused by unbalanced axial and tangential magnetic fields. With these measurements we aim at investigating the eddy current losses of commonly used former materials. A one layer cable conductor was wound on a glass fibre reinforced polymer (GRFP) former. By inserting a variety of materials into this, it was possible to measure the eddy current losses of each of the former candidates separately; for example copper tubes, stainless steel braid, copper braid, corrugated stainless steel tubes, etc. The measured data are compared with the predictions of a theoretical model. Our results show that in most cases, the losses induced by eddy currents in the former are negligible. However, for materials with a low resistivity the eddy current losses may become significant, e.g. for high purity Cu or Al.