We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels. We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R∼18.6, corresponding to z∼0.2. Galaxies were assigned spectral types based on emission-line strengths. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15≲z≲0.5; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05≲z≲0.2; starbursting galaxies are a small fraction (∼6 per cent), and are very nearby (z≲0.05). Some 9 per cent of the population have Seyfert 1/quasar-type spectra, all at z≳0.8, and 4 per cent are Seyfert 2 type galaxies at intermediate redshifts (z∼0.2).
Using our measurements and data from the Phoenix survey (Hopkins et al.), we obtain an estimate for N(z) at S1.4 GHz≥1 mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up ≲5 per cent of the radio population at S∼1 mJy.