We use redshift determinations and spectral analysis of galaxies in the 2dF Galaxy Redshift Survey to study the properties of local radio sources with S ≥ 1 mJy. 557 objects (hereafter called the spectroscopic sample) drawn from the FIRST survey, corresponding to 2.3 per cent of the total radio sample, are found in the 2dFGRS catalogue within the area 9h48m ≲ RA(2000) ≲ 14h32m and -2o.77 ≲ Dec.(2000) ≲ 2o.25, down to a magnitude limit bJ = 19.45. The excellent quality of 2dF spectra allows us to divide these sources into classes, according to their optical spectra. Absorption-line systems make up 63 per cent of the spectroscopic sample. These may or may not show emission lines due to AGN activity, and correspond to 'classical' radio galaxies belonging mainly to the FRI class. They are characterized by relatively high radio-to-optical ratios, red colours, and high radio luminosities (1021 ≲ P1.4 GHz/W Hz-1 sr-1 ≲ 1024). Actively star-forming galaxies contribute about 32 per cent of the sample. These objects are mainly found at low redshifts (z ≲ 0.1) and show low radio-to-optical ratios, blue colours and low radio luminosities. We also found 18 Seyfert 2 galaxies (3 per cent) and four Seyfert 1s (1 per cent). Analysis of the local radio luminosity function (LF) shows that radio galaxies are well described by models that assume pure luminosity evolution, at least down to radio powers P1.4 GHz ≲ 1020.5 W Hz-1 sr-1. Late-type galaxies, whose relative contribution to the radio LF is found to be lower than was predicted by previous works, present an LF which is comparable with the IRAS galaxy LF. This class of sources therefore plausibly constitutes the radio counterpart of the dusty spirals and starbursts that dominate the counts at 60 μm.