We are studying the Na-O anticorrelation in several globular clusters of different Horizontal Branch ( HB ) morphology in order to derive a possible relation between ( primordial ) chemical inhomogeneities and morphological parameters of the cluster population . We used the multifiber spectrograph FLAMES on the ESO Very Large Telescope UT2 and derived atmospheric parameters and elemental abundances of Fe , O and Na for about 150 red giant stars in the Galactic globular cluster NGC 6752 . The average metallicity we derive is [ Fe/H ] = - 1.56 , in agreement with other results from red giants , but lower than obtained for dwarfs or early subgiants . In NGC 6752 there is not much space for an intrinsic spread in metallicity : on average , the rms scatter in [ Fe/H ] is 0.037 \pm 0.003 dex , while the scatter expected on the basis of the major error sources is 0.039 \pm 0.003 dex . The distribution of stars along the Na-O anticorrelation is different to what was found in the first paper of this series for the globular cluster NGC 2808 : in NGC 6752 it is skewed toward more Na-poor stars , and it resembles more the one in M 13 . Detailed modeling is required to clarify whether this difference may explain the very different distributions of stars along the HB .