(abridged) The aim of this paper is to investigate the metallicity dependence of the PL relation in V and K, based on a sample of 128 Galactic, 36 LMC, and 6 SMC Cepheids with individual Baade-Wesselink (BW) distances and individually determined metallicities from high-resolution spectroscopy. The p-relation finally adopted is 1.50 -0.24log P. The slope of this relation is based on the condition that the distance to the LMC does not depend on period or (V-K) colour and that the slope of the PL

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... elation based on the BW distances agrees with that based on apparent magnitude. The zero point of the relation is tight to the Cepheids with HST and revised Hipparcos parallaxes as well as to Cepheids in clusters. The slope of the Galactic and LMC K-band relation formally agrees within the errors, and combining all Cepheids (including the SMC) results in a negligible metallicity dependence. A similar conclusion is found for the reddening-free Wesenheit relation. In the V-band the situation is more complex. The slope of the LMC and the Galactic PL relation differ at the 3sigma level. Combining the sample nevertheless results in a metallicity term significant at the 2sigma level. The details of the comparison of BW-based distances and Cepheids with HST and revised Hipparcos parallaxes also play a role. The method used by Storm et al. would lead to larger DM of 18.37 and 18.81 for the LMC and SMC, respectively. The LMC DM is shorter than the currently accepted value, which is in the range 18.42 to 18.55 (Walker 2012), and it is speculated that the p-factor may depend on metallicity.