We investigate the luminosity-metallicity (L-Z) relation in the local Universe (0 < 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 starforming galaxies from active galactic nuclei (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 ([O II] λ3727, [O III] λ5007 and Hβ) 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 following bright emission lines [O II] λ3727, [O III] λ5007 and Hβ (parameters R 23 and O 32) to O/H. We used the [N II] λ6584/Hα emission-line ratio as a 'secondary' abundance indicator to break the degeneracy between O/H and R 23. We confirm the existence of the L-Z relation over a large range of abundances (∼2 dex) and luminosities (∼9 mag). 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 that derived by Melbourne and Salzer using the Kitt Peak National Observatory (KPNO) International Spectroscopic Survey (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 L-Z relation will be used as the local 'reference' for future studies of the evolution with cosmic time of fundamental galaxy scaling relations.