We performed a large spectroscopic survey of compact, unresolved objects in the core of the Hydra I galaxy cluster (Abell 1060), with the aim of identifying ultra-compact dwarf galaxies (UCDs), and investigating the properties of the globular cluster (GC) system around the central cD galaxy NGC 3311. We obtained VIMOS medium resolution spectra of about 1200 candidate objects with apparent magnitudes 18.5 < V < 24.0 mag, covering both the bright end of the GC luminosity function and the luminosity range of all known UCDs. By means of spectroscopic redshift measurements, we identified 118 cluster members, from which 52 are brighter than M_V = -11.0 mag, and can therefore be termed UCDs. The brightest UCD in our sample has an absolute magnitude of M_V = -13.4 mag (corresponding to a mass of > 5 x 10^7 M_sun) and a half-light radius of 25 pc. This places it among the brightest and most massive UCDs ever discovered. Most of the GCs/UCDs are both spatially and dynamically associated to the central cD galaxy. The overall velocity dispersion of the GCs/UCDs is comparable to what is found for the cluster galaxies. However, when splitting the sample into a bright and a faint part, we observe a lower velocity dispersion for the bright UCDs/GCs than for the fainter objects. At a dividing magnitude of M_V = -10.75 mag, the dispersions differ by more than 200 km/s, and up to 300 km/s for objects within 5 arcmin around NGC 3311. We interpret these results in the context of different UCD formation channels, and conclude that interaction driven formation seems to play an important role in the centre of Hydra I.
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