We performed a comprehensive study of the stellar populations in the young Large Magellanic Cloud cluster NGC 1866, combining the analysis of its best-studied Cepheids with that of a very accurate colour–magnitude diagram (CMD) obtained from the most recent Hubble Space Telescope photometry. We used a Bayesian method based on new PARSEC stellar evolutionary tracks with overshooting and rotation to obtain ages and initial rotation velocities of five well-studied Cepheids of the cluster. We find that four of the five Cepheids belong to an initially slowly rotating young population (of 176 ± 5 Myr), while the fifth is significantly older, either 288 ± 20 Myr for models with high initial rotational velocity (ω_i ∼ 0.9), or 202 ± 5 Myr for slowly rotating models. The complementary analysis of the CMD rules out the latter solution while strongly supporting the presence of two distinct populations of ∼176 Myr and ∼288 Myr, respectively. Moreover, the observed multiple main sequences and the turn-offs indicate that the younger population is mainly made of slowly rotating stars, as is the case of the four younger Cepheids, while the older population is made mainly of initially fast rotating stars, as is the case of the fifth Cepheid. Our study reinforces the notion that some young clusters like NGC 1866 harbour multiple populations. This work also hints that the first population, i.e. the older, may inherit the angular momentum from the parent cloud while stars of the second population, i.e. the younger, do not.