We investigate the Luminosity-Metallicity (L-Z) relation in the local universe (z < 0.15) using spectra of 6387 star-forming galaxies extracted from the 2dF Galaxy Redshift Survey. This sample is by far the largest to date used to perform such a study. We distinguish star-forming galaxies from AGNs using "standard" diagnostic diagrams to build a homogeneous sample of starburst galaxies for the L-Z study. We propose new diagnostic diagrams using "blue" emission lines ([OII]3727, [OIII]5007 and Hbeta) only to discriminate starbursts from AGNs in intermediate-redshift (z > 0.3) galaxies. Oxygen-to-hydrogen (O/H) abundance ratios are estimated using the "strong-line" method, which relates the strength of bright emission lines (parameters R23 and O32) to O/H. We confirm the existence of the luminosity-metallicity relation over a large range of abundances (~ 2 dex) and luminosities (~ 9 magnitudes). We find a linear relation between the gas-phase oxygen abundance and both the "raw" and extinction-corrected absolute B-band magnitude with a rms of 0.27. A similar relation, with nearly the same scatter, is found in the R band. This relation is in good agreement with the one derived by Melbourne & Salzer (2002) using the KISS data. However, our L-Z relation is much steeper than previous determinations using samples of "normal" irregular and spiral galaxies. This difference seems to be primarily due to the choice of the galaxy sample used to investigate the L-Z relation rather than any systematic error affecting the O/H determination. We anticipate that this luminosity-metallicity relation will be used as the local "reference" for future studies of the evolution with cosmic time of fundamental galaxy scaling relations. (Abridged version). Comment: 11 pages, 9 figures. Accepted for publication in MNRAS