We present new near-IR light curves for six Cepheids in the young blue LMC cluster NGC 1866 as well as high precision radial velocity curves for ten Cepheids in NGC 1866 and two in NGC 2031. For the six Cepheids in NGC 1866 with new J and K light curves we determine distances and absolute magnitudes by applying the near-IR surface brightness method. We find that the formal error estimates on the derived distances are underestimated by about a factor of two. We find excellent agreement between the absolute magnitudes for the low metallicity LMC Cepheids with the Period-Luminosity (P-L) relation determined by the near-IR surface brightness (ISB) method for Galactic Cepheids suggesting that the slope of the P-L relations for low metallicity and solar metallicity samples could be very similar in contrast to other recent findings. Still there appears to be significant disagreement between the observed slopes of the OGLE based apparent P-L relations in the LMC and the slopes derived from ISB analysis of Galactic Cepheids, and by inference for Magellanic Cloud Cepheids, indicating a possible intrinsic problem with the ISB method itself. Resolving this problem could reaffirm the P-L relation as the prime distance indicator applicable as well to metallicities significantly different from the LMC value.