The X-ray spectra of many active galactic nuclei (AGN) show a soft X-ray excess below 1-2 keV on top of the extrapolated high- energy power law. The origin of this component is uncertain. It could be a signature of relativistically blurred, ionized reflection, or the high-energy tail of thermal Comptonization in a warm (kT $sim$ 1 keV), optically thick ($tausimeq$ 10-20) corona producing the optical/UV to soft X-ray emission. The purpose of the present paper is to test the warm corona model on a statistically significant sample of unabsorbed, radio-quiet AGN with XMM-newton archival data, providing simultaneous optical/UV and X-ray coverage. The sample has 22 objects and 100 observations. We use two thermal comptonization components to fit the broad-band spectra, one for the warm corona emission and one for the high-energy continuum. In the optical-UV, we also include the reddening, the small blue bump and the Galactic extinction. In the X-rays, we include a WA and a neutral reflection. The model gives a good fit (reduced $chi^2 <1.5$) to more than 90% of the sample. We find the temperature of the warm corona to be uniformly distributed in the 0.1-1 keV range, while the optical depth is in the range $sim$10-40. These values are consistent with a warm corona covering a large fraction of a quasi-passive accretion disc, i.e. that mostly reprocesses the warm corona emission. The disk intrinsic emission represents no more than 20% of the disk total emission. According to this interpretation, most of the accretion power would be released in the upper layers of the accretion flow.