Metallicities ([Fe/H]) from low resolution spectroscopy obtained with the Very Large Telescope (VLT) are presented for 98 RR Lyrae and 3 short period Cepheids in the bar of the Large Magellanic Cloud. Our metal abundances have typical errors of +/-0.17 dex. The average metallicity of the RR Lyrae stars is [Fe/H]=-1.48 +/- 0.03 +/- 0.06 on the scale of Harris (1996). The star-to-star scatter (0.29 dex) is larger than the observational errors, indicating a real spread in metal abundances. The derived metallicities cover the range -2.12 < [Fe/H] <-0.27, but there are only a few stars having [Fe/H] > -1. For the ab-type variables we compared our spectroscopic abundances with those obtained from the Fourier decomposition of the light curves. We find good agreement between the two techniques, once the systematic offset of 0.2 dex between the metallicity scales used in the two methods is taken into account. The spectroscopic metallicities were combined with the dereddened apparent magnitudes of the variables to derive the slope of the luminosity-metallicity relation for the LMC RR Lyrae stars: the resulting value is 0.214 +/- 0.047 mag/dex. Finally, the 3 short period Cepheids have [Fe/H] values in the range -2.0 < [Fe/H] <-1.5 . They are more metal-poor than typical LMC RR Lyrae stars, thus they are more likely to be Anomalous Cepheids rather than the short period Classical Cepheids that are being found in a number of dwarf Irregular galaxies.