Several independent lines of evidence now point to a connection between the physical processes that govern radio ( i.e . jet ) and X–ray emission from accreting X–ray binaries . We present a comprehensive study of ( quasi– ) simultaneous radio : X–ray observations of stellar black hole binaries during the spectrally hard X–ray state , finding evidence for a strong correlation between these two bands over more than three orders of magnitude in X–ray luminosity . The correlation extends from the quiescent regime up to close to the soft state transition , where radio emission starts to decline , sometimes below detectable levels , probably corresponding to the physical disappearance of the jet . The X–ray transient V 404 Cygni is found to display the same functional relationship already reported for GX 339–4 between radio and X–ray flux , namely S _ { radio } \propto S _ { X } ^ { +0.7 } . In fact the data for all low/hard state black holes is consistent with a universal relation between the radio and X–ray luminosity of the form L _ { radio } \propto L _ { X } ^ { +0.7 } . Under the hypothesis of common physics driving the disc–jet coupling in different sources , the observed spread to the best–fit relation can be interpreted in terms of a distribution in Doppler factors and hence used to constrain the bulk Lorentz factors of both the radio and X–ray emitting regions . Monte Carlo simulations show that , assuming little or no X–ray beaming , the measured scatter in radio power is consistent with Lorentz factors \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 2 for the outflows in the low/hard state , significantly less relativistic than the jets associated with X–ray transients . When combined radio and X–ray beaming is considered , the range of possible jet bulk velocities significantly broadens , allowing highly relativistic outflows , but implying therefore severe X–ray selection effects . If the radio luminosity scales as the total jet power raised to x > 0.7 , then there exists an X–ray luminosity below which most of the accretion power will be channelled into the jet , rather than in the X–rays . For x = 1.4 , as in several optically thick jet models , the power output of ‘ quiescent ’ black holes may be jet–dominated below L _ { X } \simeq 4 \times 10 ^ { -5 } L _ { Edd } .