We report the results of an observation of Cygnus X-1 with INTEGRAL, that we combine with simultaneous radio observations with the Ryle telescope. Both spectral and variability properties of the source indicate that Cygnus X-1 was in an Intermediate State. The INTEGRAL spectrum shows a high-energy cut-off or break around 100 keV. The shape of this cut-off differs from pure thermal Comptonisation, suggesting the presence of a non-thermal component at higher energies.The average broad band spectrum is well represented by hybrid thermal/non-thermal Comptonisation models. During the 4 day long observation the source showed an important spectral and flux variability. A principal component analysis demonstrates that most of this variability occurs through 2 independent modes. The first mode consists in changes in the overall luminosity on time scale of hours with almost constant spectra that are strikingly uncorrelated with the variable radio flux. We interpret this variability mode as variations of the dissipation rate in the corona. The second variability mode consists in a pivoting of the spectrum around 10 keV. It acts on a longer time-scale: initially soft, the spectrum hardens in the first part of the observation and then softens again. This pivoting pattern is strongly correlated with the radio (15 GHz) emission: radio fluxes are stronger when the INTEGRAL spectrum is harder. We propose that the pivoting mode represents a mini state transition from a nearly High Soft State to a nearly Low Hard State, and back. This mini-transition would be caused by changes in the soft cooling photons flux in the hot Comptonising plasma associated with an increase of the temperature of the accretion disc. The jet power then appears to be anti-correlated with the disc luminosity and unrelated to the coronal power.
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