Pre-main sequence models with inflated radii are needed to simultaneously reproduce the colour-magnitude diagram and the lithium depletion pattern in young open clusters. We test a new set of PMS models including radius inflation due to starspots or to magnetic inhibition of convection, using five clusters observed by the Gaia-ESO Survey, spanning the age range ~10-100 Myr where such effects could be important. Gaia-ESO radial velocities are combined with Gaia EDR3 astrometry to obtain clean lists of high-probability members for the five clusters. A Bayesian maximum likelihood method is adopted to derive the best model parameters and the cluster reddening and age. Models are calculated for different values of the mixing length parameter ($\alpha_{ML}=2.0$, 1.5 and 1.0), without spots or with effective spot coverage $\beta_{spot}=0.2$ and 0.4. To reproduce the CMD and the Li depletion pattern in Gamma Vel A and B and in 25 Ori we need both a reduced convection efficiency $\alpha_{ML}=1.0$ and an effective spot coverage of ~20%. We obtained ages of 18 Myr and 21 Myr for Gamma Vel A and B, respectively, and 19 Myr for 25 Ori. However, a single isochrone is not sufficient to account for the Li dispersion, and an increasing level of spot coverage as mass decreases seems to be required. The older clusters (NGC2451B at 30 Myr, NGC2547 at 35 Myr, and NGC2516 at 138 Myr) are consistent with standard models, with $\alpha_{ML}=2.0$ and no spots, except at low masses: a 20% spot coverage seems to better reproduce the sequence of M-type stars and might explain the observed abundance spread. The quality of Gaia-ESO data combined with Gaia allows us to gain important insights on PMS evolution. Models including starspots can provide a consistent explanation of the cluster sequences and Li abundances of young clusters, although a range of starspot coverage is required to fully reproduce the data.