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(abridged) Recent investigations aimed at estimating the distance to theyoung LMC cluster NGC1866 have made use of Red Clump stars in the surroundingLMC field, together with empirical and theoretical Main-Sequence fittingmethods, and have found significantly different distances for the field and thecluster, the latter being closer by in distance modulus by \Delta (DM) \sim0.20 mag. In this paper we (re-)consider the Cepheid star population ofNGC1866, to try to shed some light on this discrepancy. By combining variousextensive photometric datasets in BVI and single-epoch 2MASS JHK photometry, PLrelationships for the cluster Cepheids are obtained. A comparison between thefield LMC and cluster PL relationships for the reddening free Wesenheit indexgives a firm determination of the distance between the cluster and the LMC mainbody (0.04 mag in distance modulus, the cluster being more distant) which,coupled to a model for the geometry of the LMC disk, provides \Delta (DM)ranging between 0.0 and -0.11 mag. The simultaneous comparison of the PLrelationships in BVI for the cluster and LMC field gives an estimate of thecluster reddening, which results to be E(B-V) = 0.12 \pm 0.02. Thisdetermination is higher than the canonical value of 0.06 mag used in allprevious studies, but we show that it is not in contradiction with are-analysis of independent estimates. The cluster Main Sequence fittingdistance obtained with this new reddening is DM = 18.58 \pm 0.08, fullycompatible with the Red Clump value of DM = 18.53 \pm0.07(random)^{+0.02}_{-0.05} (systematic) and the Cepheid constraint on \Delta(DM).Comment: accepted for A&

The distance to the LMC cluster NGC 1866; clues from the cluster Cepheid population