Ionisation cluster size distributions produced in the sensitive volume of an ion-counting wall-less nanodosimeter by monoenergetic carbon ions with energies between 45 MeV and 150 MeV were measured at the TANDEM-ALPI ion accelerator facility complex of the LNL INFN in Legnaro. Those produced by monoenergetic helium ions with energies between 2 MeV and 20 MeV were measured at the accelerator facilities of PTB and with a 241Am alpha particle source. C3H8 was used as the target gas. The ionisation cluster size distributions were measured in narrow beam geometry with the primary beam passing the target volume at specified distances from its centre, and in broad beam geometry with a fan-like primary beam. By applying a suitable drift time window, the effective size of the target volume was adjusted to match the size of a DNA segment. The measured data were compared with the results of simulations obtained with the PTB Monte Carlo code PTra. Before the comparison, the simulated cluster size distributions were corrected with respect to the background of additional ionisations produced in the transport system of the ionised target gas molecules. Measured and simulated characteristics of the particle track structure are in good agreement for both types of primary particles and for both types of the irradiation geometry. ; Comment: 25 pages, 20 figures