We select a sample of low-redshift (z~ 0.1) E+A galaxies from the 2dF Galaxy Redshift Survey (2dFGRS). The spectra of these objects are defined by strong hydrogen Balmer absorption lines (Hδ, Hγ, Hβ) combined with a lack of [OII] 3727-Åemission, together implying a recently truncated burst of star formation. The E+A spectrum is thus a signpost to galaxies in the process of evolution. We quantify the local environments, clustering properties and luminosity function of the E+A galaxies. We find that the environments are consistent with the ensemble of 2dFGRS galaxies: low-redshift E+A systems are located predominantly in the field, existing as isolated objects or in poor groups. However, the luminosity distribution of galaxies selected using three Balmer absorption lines Hδγβ appears more typical of ellipticals. Indeed, morphologically these galaxies are preferentially spheroidal (E/S0) systems. In a small but significant number we find evidence for recent major mergers, such as tidal tails. We infer that major mergers are one important formation mechanism for E+A galaxies, as suggested by previous studies. At low redshift the merger probability is high in the field and low in clusters, thus these recently formed spheroidal systems do not follow the usual morphology-density relation for ellipticals. Regarding the selection of E+A galaxies: we find that basing the Balmer-line criterion solely on Hδ absorption leads to a significant subpopulation of disc systems with detectable Hα emission. In these objects the [OII] emission is presumably either obscured by dust or present with a low signal-to-noise ratio, whilst the (Hγ, Hβ) absorption features are subject to emission-filling.