  Rapidly rotating, low-mass members of eclipsing binary systems have measured
radii significantly larger than predicted by standard models. It has been
proposed that magnetic activity is responsible for radius inflation. By
estimating the radii of low-mass stars in three young clusters (NGC 2264, NGC
2547, NGC 2516, with ages of 5, 35 and 140 Myr respectively), we aim to
establish whether similar radius inflation is seen in single, magnetically
active stars. We use radial velocities from the Gaia-ESO Survey (GES) and
published photometry to establish cluster membership and combine GES
measurements of vsini with published rotation periods to estimate average radii
for groups of fast-rotating cluster members as a function of their luminosity
and age. The average radii are compared with the predictions of both standard
evolutionary models and variants that include magnetic inhibition of convection
and starspots. At a given luminosity, the stellar radii in NGC 2516 and NGC
2547 are larger than predicted by standard evolutionary models at the ages of
these clusters. The discrepancy is least pronounced and not significant ~10
percent) in ZAMS stars with radiative cores, but more significant in
lower-mass, fully convective pre main-sequence cluster members, reaching
30+/-10 percent. The uncertain age and distance of NGC 2264 preclude a reliable
determination of any discrepancy for its members. The median radii we have
estimated for low-mass fully convective stars in the older clusters are
inconsistent (at the 2-3 sigma level) with non-magnetic evolutionary models and
more consistent with models that incorporate the effects of magnetic fields or
dark starspots. The available models suggest this requires either surface
magnetic fields exceeding 2.5 kG, spots that block about 30 per cent of the
photospheric flux, or a more moderate combination of both. [Abridged]
