The HARP experiment was designed to study hadron production in proton-nucleus collisions in the energy range of 1.5 GeV/c–15 GeV/c. The experiment was made of two spectrometers, a forward dipole spectrometer and a large-angle solenoid spectrometer. In the large-angle spectrometer the main tracking and particle identification is performed by a cylindrical Time Projection Chamber (TPC) which suffered a number of shortcomings later addressed in the analysis. In this paper we discuss the effects of time-dependent (dynamic) distortions of the position measurements in the TPC which are due to a build-up of ion charges in the chamber during the accelerator spill. These phenomena have been studied both by modelling and by experiment, and a correction procedure has been developed. The effects of the time-dependent distortions have been measured experimentally by means of recoil protons in elastic scattering reactions, where the track coordinates are precisely predictable from simple kinematical considerations. The dynamics of the positive ion cloud and of the electrostatics of the field-cage system have been modelled with a phenomenological approach providing an understanding of the features. Using the elastic scattering data a general correction procedure has been developed and applied to all data settings. After application of the corrections for dynamic distortions the corrected data have a performance equal to data where the dynamic distortions are absent. We describe the phenomenological model, the comparison with the measurements, the distortion correction method and the results obtained with experimental data.