Objective. The purpose of this study is to estimate the energy and angular distribution of secondary neutrons inside a phantom in hadron therapy, which will support decisions on detector choice and experimental setup design for in-phantom secondary neutron measurements. Approach. Dedicated Monte Carlo simulations were implemented, considering clinically relevant energies of protons, helium and carbon ions. Since scored quantities can vary from different radiation transport models, the codes FLUKA, TOPAS and MCNP were used. The geometry of an active scanning beam delivery system for heavy ion treatment was implemented, and simulations of pristine and spread-out Bragg peaks were carried out. Previous studies, focused on specific ion types or single energies, are qualitatively in agreement with the obtained results. Main results. The secondary neutrons energy distributions present a continuous spectrum with two peaks, one centred on the thermal/epithermal region, and one on the high-energy region, with the most probable energy ranging from 19 up to 240 MeV, depending on the ion type and its initial energy. The simulations show that the secondary neutron energies may exceed 400 MeV and, therefore, suitable neutron detectors for this energy range shall be needed. Additionally, the angular distribution of the low energy neutrons is quite isotropic, whereas the fast/relativistic neutrons are mainly scattered in the down-stream direction. Significance. It would be possible to minimize the influence of the heavy ions when measuring the neutron-generated recoil protons by selecting appropriate measurement positions within the phantom. Although there are discrepancies among the three Monte Carlo codes, the results agree qualitatively and in order of magnitude, being sufficient to support further investigations with the ultimate goal of mapping the secondary neutron doses both in- and out-of-field in hadrontherapy. The obtained secondary neutron spectra are available as supplementary material.