The centre of the Milky Way galaxy, approximately 8 kpc from the Earth, is a peculiar region due to its high density of stars, the resulting amount of stellar activity, and the presence of a supermassive black hole. A puzzling observation is the ionisation rate in the Central Molecular Zone which has been measured using different methods along several lines of sight. The estimated average value over this central region is 3-4 orders of magnitude higher than the local ionisation rate. As electromagnetic radiation can not penetrate the high gas column densities, cosmic rays are assumed to be the main ionising agents in this region. This unusually high ionisation rate should then reveal an equally high cosmic-ray density in this region. However, this excess is not reflected in the gamma-ray emissions that constrain the high-energy cosmic-ray spectrum. In this work, we explore the Galactic Centre ionisation scenario in which cosmic-ray protons and electrons are the exclusive ionising agents. We use a custom particle-transport simulation to model the interactions of cosmic rays with the surrounding medium and infer the necessary particle injection conditions. We find that the injection spectrum needs to be very steep. We also find that a significant fraction of the power in cosmic rays available in the entire galaxy needs to be injected in only the central 100 parsecs. We conclude that cosmic rays can not be the only ionising agents in the Galactic Centre, thereby casting doubt on a hitherto unquestioned paradigm.