We have carried out a spectroscopic survey of low-redshift galaxy systems identified by the matched-filter technique in a moderately deep I-band survey. We present new redshifts for 747 galaxies in 23 ESO Imaging Survey (EIS) cluster fields. We use the "gap"-technique to search for significant overdensities in redshift space for identifying groups/clusters of galaxies corresponding to the original EIS matched-filter cluster candidates. In this way we spectroscopically confirm systems in 10 of the 23 cluster candidate fields with a matched-filter estimated redshift z_MF_=0.3-0.4 and with spectroscopic redshifts in the range from z=0.158 to z=0.534, with the observations favouring the confirmation of systems at the lower redshift end. After careful analysis of the redshift distribution, one system was split into two very close clumps in redshift space. We find that the systems identified in the present paper span a broad range of velocity dispersion and richness. The measured one-dimensional velocity dispersion range from 175km/s to 497km/s, consistent with the values obtained in previous papers using much larger samples for systems over the same redshift range. Both undersampling and contamination by substructures contribute to the uncertainty of these measurements. The richness range corresponds to clusters with an estimated total luminosity in the range 12L^*^-65L^*^, but these estimates are very uncertain as are their relation to the velocity dispersion (mass) of the systems. From the analysis of the colours of the galaxy populations we find that ~60% of the spectroscopically confirmed systems have a "significant" red sequence. We find that the colour of the red sequence galaxies matches passive stellar evolution predictions. With this paper we complete our spectroscopic survey of the fields of 58 EIS cluster candidates with estimated redshifts z<=0.4 (see also Hansen et al., 2002, Cat. <J/A+A/388/1>; Olsen et al., 2003, Cat. <J/A+A/409/439>, Olsen et al., 2005, Cat. <J/A+A/435/781>). We have measured a total of 1954 galaxy redshifts in the range z=0.0065 to z=0.6706. Of the 58 systems we confirm 42 (~75%) with redshifts between z=0.095 and z=0.534.