We have carried out a study of known clusters within the 2dF Galaxy Redshift Survey (2dFGRS) observed areas and have identified 431 Abell, 173 APM and 343 EDCC clusters. Precise redshifts, velocity dispersions and new centroids have been measured for the majority of these objects, and this information is used to study the completeness of these catalogues, the level of contamination from foreground and background structures along the cluster's line of sight, the space density of the clusters as a function of redshift, and their velocity dispersion distributions. We find that the Abell and EDCC catalogues are contaminated at the level of about 10 per cent, whereas the APM catalogue suffers only 5 per cent contamination. If we use the original catalogue centroids, the level of contamination rises to approximately 15 per cent for the Abell and EDCC catalogues, showing that the presence of foreground and background groups may alter the richness of clusters in these catalogues. There is a deficiency of clusters at z ∼ 0.05 that may correspond to a large underdensity in the Southern hemisphere. From the cumulative distribution of velocity dispersions for these clusters, we derive a space density of σ > 1000kms-1 clusters of 3.6 × 10-6 h3 Mpc-3. This result is used to constrain models for structure formation; our data favour low-density cosmologies, subject to the usual assumptions concerning the shape and normalization of the power spectrum.