Context. Some of the most prominent sources for particle acceleration in our Solar System are large eruptions of magnetised plasma from the Sun called coronal mass ejections (CMEs). These accelerated particles can generate radio emission through various mechanisms. Aims. CMEs are often accompanied by a variety of solar radio bursts with different shapes and characteristics in dynamic spectra. Radio bursts directly associated with CMEs often show movement in the direction of CME expansion. Here, we aim to determine the emission mechanism of multiple moving radio bursts that accompanied a flare and CME that took place on 14 June 2012. Methods. We used radio imaging from the Nançay Radioheliograph, combined with observations from the Solar Dynamics Observatory and Solar Terrestrial Relations Observatory spacecraft, to analyse these moving radio bursts in order to determine their emission mechanism and three-dimensional (3D) location with respect to the expanding CME. Results. In using a 3D representation of the particle acceleration locations in relation to the overlying coronal magnetic field and the CME propagation, for the first time, we provide evidence that these moving radio bursts originate near the CME flanks and some that are possible signatures of shock-accelerated electrons following the fast CME expansion in the low corona. Conclusions. The moving radio bursts, as well as other stationary bursts observed during the eruption, occur simultaneously with a type IV continuum in dynamic spectra, which is not usually associated with emission at the CME flanks. Our results show that moving radio bursts that could traditionally be classified as moving type IVs can represent shock signatures associated with CME flanks or plasma emission inside the CME behind its flanks, which are closely related to the lateral expansion of the CME in the low corona. In addition, the acceleration of electrons generating this radio emission appears to be favoured at the CME flanks, where the CME encounters coronal streamers and open field regions.