We demonstrate a novel method to purge the core of long lengths of hollow-core optical fibres where the original gas content is pushed out by helium permeating through the fibre jacket along the full fibre length. Once helium has replaced the gas in the fibre, the fibre ends can be sealed, whereupon the helium is left to permeate back out through the glass, leaving an evacuated fibre. The viability and the limits of this technique are investigated by a numerical analysis whose accuracy is validated by proof-of-principle experiments. The model predicts that the evacuation times of hollow-core fibres of hundreds of metres to kilometres length can be reduced by orders of magnitude compared to traditional methods, from hundreds of days to about one day.