  We present homogeneous and accurate iron abundances for 42 Galactic Cepheids
based on high-spectral resolution (R~38,000) high signal-to-noise ratio
(SNR>100) optical spectra collected with UVES at VLT (128 spectra). The above
abundances were complemented with high-quality iron abundances provided either
by our group (86) or available in the literature. We paid attention in deriving
a common metallicity scale and ended up with a sample of 450 Cepheids. We also
estimated for the entire sample accurate individual distances by using
homogeneous near-infrared photometry and the reddening free Period-Wesenheit
relations. The new metallicity gradient is linear over a broad range of
Galactocentric distances (Rg~5-19 kpc) and agrees quite well with similar
estimates available in the literature (-0.060+/-0.002 dex/kpc). We also uncover
evidence which suggests that the residuals of the metallicity gradient are
tightly correlated with candidate Cepheid Groups (CGs). The candidate CGs have
been identified as spatial overdensities of Cepheids located across the thin
disk. They account for a significant fraction of the residual fluctuations, and
in turn for the large intrinsic dispersion of the metallicity gradient. We
performed a detailed comparison with metallicity gradients based on different
tracers: OB stars and open clusters. We found very similar metallicity
gradients for ages younger than 3 Gyrs, while for older ages we found a
shallower slope and an increase in the intrinsic spread. The above findings
rely on homogeneous age, metallicity and distance scales. Finally we found, by
using a large sample of Galactic and Magellanic Cepheids for which are
available accurate iron abundances, that the dependence of the luminosity
amplitude on metallicity is vanishing.
