  We report the first observation of a transient relativistic jet from the
canonical black hole candidate, Cygnus X-1, obtained with the Multi-Element
Radio-Linked Interferometer Network (MERLIN). The jet was observed in only one
of six epochs of MERLIN imaging of the source during a phase of repeated X-ray
spectral transitions in 2004 Jan--Feb, and this epoch corresponded to the
softest 1.5-12 keV X-ray spectrum. With only a single epoch revealing the jet,
we cannot formally constrain its velocity. Nevertheless, several lines of
reasoning suggest that the jet was probably launched 0.5-4.0 days before this
brightening, corresponding to projected velocities of 0.2c < v_app < 1.6c, and
an intrinsic velocity of > 0.3c. We also report the occurrence of a major radio
flare from Cyg X-1, reaching a flux density of ~120 mJy at 15 GHz, and yet not
associated with any resolvable radio emission, despite a concerted effort with
MERLIN. We discuss the resolved jet in terms of the recently proposed 'unified
model' for the disc-jet coupling in black hole X-ray binaries, and tentatively
identify the 'jet line' for Cyg X-1. The source is consistent with the model in
the sense that a steady jet appears to persist initially when the X-ray
spectrum starts softening, and that once the spectral softening is complete the
core radio emission is suppressed and transient ejecta / shock observed.
However, there are some anomalies, and Cyg X-1 clearly does not behave like a
normal black hole transient in progressing to the canonical soft / thermal
state once the ejection event has happened.
