The Fornax Cluster Spectroscopic Survey (FCSS) project utilizes the Two‐degree Field (2dF) multi‐object spectrograph on the Anglo‐Australian Telescope (AAT). Its aim is to obtain spectra for a complete sample of all 14 000 objects with 16.5 ≤bj≤ 19.7 irrespective of their morphology in a 12 deg2 area centred on the Fornax cluster. A sample of 24 Fornax cluster members has been identified from the first 2dF field (3.1 deg2 in area) to be completed. This is the first complete sample of cluster objects of known distance with well‐defined selection limits. Nineteen of the galaxies (with −15.8 < MB < −12.7) appear to be conventional dwarf elliptical (dE) or dwarf S0 (dS0) galaxies. The other five objects (with −13.6 < MB < −11.3) are those galaxies which were described recently by Drinkwater et al. and labelled ‘ultracompact dwarfs’ (UCDs). A major result is that the conventional dwarfs all have scale sizes α≳ 3 arcsec (≃300 pc). This apparent minimum scale size implies an equivalent minimum luminosity for a dwarf of a given surface brightness. This produces a limit on their distribution in the magnitude–surface brightness plane, such that we do not observe dEs with high surface brightnesses but faint absolute magnitudes. Above this observed minimum scale size of 3 arcsec, the dEs and dS0s fill the whole area of the magnitude–surface brightness plane sampled by our selection limits. The observed correlation between magnitude and surface brightness noted by several recent studies of brighter galaxies is not seen with our fainter cluster sample. A comparison of our results with the Fornax Cluster Catalog (FCC) of Ferguson illustrates that attempts to determine cluster membership solely on the basis of observed morphology can produce significant errors. The FCC identified 17 of the 24 FCSS sample (i.e. 71 per cent) as being ‘cluster’ members, in particular missing all five of the UCDs. The FCC also suffers from significant contamination: within the FCSS's field and selection limits, 23 per cent of those objects described as cluster members by the FCC are shown by the FCSS to be background objects.