The results of 21-cm neutral hydrogen survey observations, made using the 64-m Parkes telescope, are presented for two 8 degrees by 8 degrees fields, centred on the Centaurus and Fornax galaxy clusters, and a smaller 1 degrees.5 field in Eridanus. The purpose of the observations was to search for extended H I clouds with no clear optical counterparts. 31 previously catalogued galaxies were detected, with H I parameters for 16 being listed for the first time. One previously uncatalogued dwarf galaxy ('Wombat I', J0341-3851) was found near the Fornax cluster, Australia Telescope Compact Array observations give an Hi mass of 8 x 10(7) M-. and a diameter of 4 kpc for this object, which is also visible on UKST survey plates, However, no clouds with optically invisible counterparts were detected, We deduce a 99 per cent confidence limit on the total H I density of such objects in the cluster and near-cluster environment of Omega(H I) < 10(-2)h(-1)(delta V/100 km s(-1)).