Aims. We analyse the properties of the early-type dwarf galaxy population (M V > −17 mag) in the Hydra I cluster. We investigate the galaxy luminosity function (LF), the colour-magnitude relation (CMR), and the magnitude-surface brightness relation down to M V ∼ −10 mag. Another goal of this study is to find candidates for ultra-compact dwarf galaxies (UCDs) in Hydra I. Methods. Two spectroscopic surveys performed with Magellan I/LDSS2 at Las Campanas Observatory and VLT/VIMOS, as well as deep VLT/FORS1 images in V and I bands, covering the central parts of the cluster, were examined. We identify cluster members by radial velocity measurements and select other cluster galaxy candidates by their morphology and low surface brightness. The candidates' total magnitudes and central surface brightnesses were derived from the analysis of their surface brightness profiles. To determine the faint-end slope of the LF, the galaxy number counts are completeness corrected. Results. We obtain radial velocities for 126 objects and identify 32 cluster members, of which 5 are previously uncatalogued dwarf galaxies. One possible UCD candidate with M V = −13.26 mag is found. Our sample of 100 morphologically selected dwarf galaxies with M V > −17 mag defines a CMR that extends the CMR of the giant cluster galaxies to the magnitude limit of our survey (M V ∼ −10 mag). It matches the relations found for the Local Group (LG) and the Fornax cluster dwarf galaxies almost perfectly. The Hydra I dwarf galaxies also follow a magnitude-surface brightness relation that is very similar to that of the LG dwarf galaxies. Moreover, we observe a continuous relation for dwarf galaxies and giant early-type galaxies when plotting the central surface brightness μ 0 of a Sérsic model vs. the galaxy magnitude. The effective radius is found to be largely independent of the luminosity for M V > −18 mag. It is consistent with a constant value of R e ∼ 0.8 kpc. We present the photometric parameters of the galaxies as the Hydra I Cluster Catalogue (HCC). By fitting a Schechter function to the luminosity distribution, we derive a very flat faint-end slope of the LF (α = −1.13 ± 0.04), whereas fitting a power law for M V > −14 mag gives α = −1.40 ± 0.18. Conclusions. Our findings of a continuous CMR and μ 0 − M V relation for dwarf and giant early-type galaxies suggests that they are the same class of objects. The similarity of those relations to other environments like the LG implies that internal processes could be more important for their global photometric properties than external influences.