  Classical Cepheids (DCEPs) are the first fundamental step in the calibration
of the cosmological distance ladder. Furthermore, they represent powerful
tracers in the context of Galactic studies. We have collected high-resolution
spectroscopy with UVES@VLT for a sample of 65 DCEPs. The majority of them are
the faintest DCEPs ever observed in the Milky Way. For each target, we derived
accurate atmospheric parameters, radial velocities, and abundances for 24
different species. The resulting iron abundances range between +0.3 and $-$1.1
dex with the bulk of stars at [Fe/H]$\sim-0.5$ dex. Our sample includes the
most metal-poor DCEPs observed so far with high-resolution spectroscopy. We
complement our sample with literature data obtaining a complete sample of 637
DCEPs and use Gaia Early Data Release 3 (EDR3) photometry to determine the
distance of the DCEPs from the Period-Wesenheit-Metallicity relation. Our more
external data trace the Outer arm (at Galactocentric radius
($R_{GC})\sim$16--18 kpc) which appears significantly warped. We investigate
the metallicity gradient of the Galactic disc using this large sample, finding
a slope of $-0.060 \pm 0.002$ dex kpc$^{-1}$, in very good agreement with
previous results based both on DCEPs and open clusters. We also report a
possible break in the gradient at $R_{GC}$=9.25 kpc with slopes of $-0.063 \pm
0.007$ and $-0.079 \pm 0.003$ dex kpc$^{-1}$ for the inner and outer sample,
respectively. The two slopes differ by more than 1 $\sigma$. A more homogeneous
and extended DCEPs sample is needed to further test the plausibility of such a
break.
