We show that non-magnetic models for the evolution of pre-main-sequence (PMS) stars $cannot$ simultaneously describe the colour–magnitude diagram (CMD) and the pattern of lithium depletion seen in the cluster of young, low-mass stars surrounding $\gamma$$2$ Velorum. The age of 7.5 ± 1 Myr inferred from the CMD is much younger than that implied by the strong Li depletion seen in the cluster M-dwarfs, and the Li depletion occurs at much redder colours than predicted. The epoch at which a star of a given mass depletes its Li and the surface temperature of that star are both dependent on its radius. We demonstrate that if the low-mass stars have radii ~10 per cent larger at a given mass and age, then both the CMD and the Li-depletion pattern of the Gamma Velorum cluster are explained at a common age of $\simeq$18–21 Myr. This radius inflation could be produced by some combination of magnetic suppression of convection and extensive cool starspots. Models that incorporate radius inflation suggest that PMS stars, similar to those in the Gamma Velorum cluster, in the range 0.2 < $M$/$M\odot$ < 0.7, are at least a factor of 2 older and ~7 per cent cooler than previously thought and that their masses are much larger (by >30 per cent) than inferred from conventional, non-magnetic models in the Hertzsprung–Russell diagram. Systematic changes of this size may be of great importance in understanding the evolution of young stars, disc lifetimes and the formation of planetary systems.