  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.
