This paper is part of a series reporting the results of the ATESP radio survey obtained at 1.4 GHz with the Australia Telescope Compact Array .
The survey consists of 16 radio mosaics with \sim 8 \arcsec \times 14 \arcsec resolution and uniform sensitivity ( 1 \sigma noise level \sim 79 \mu Jy ) over the whole area of the ESO Slice Project redshift survey ( \sim 26 sq .
degrees at \delta \sim - 40 \degr ) .
The ATESP survey has produced a catalogue of 2960 radio sources down to a flux limit ( 6 \sigma ) of \sim 0.5 mJy . In this paper we present the 1.4 GHz \log N - \log S relation derived from the ATESP radio source catalogue .
The possible causes of incompleteness at the faint end of the source counts are extensively discussed and their effects are quantified and corrected for .
The ATESP counts are consistent with others reported in the literature , even though some significant discrepancies are present at low fluxes ( below a few mJy ) .
We investigate whether such discrepancies may be explained in terms of field-to-field anisotropies , considering the fact that all the existing sub-mJy surveys cover small areas of sky ( from a fraction of square degree to a few square degrees ) .
We stress that the ATESP survey , covering 26 sq .
degrees , provides the best determination of source counts available today in the flux range 0.7 \la S _ { 1.4 GHz } \la 2 mJy .