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 V404 Cygni is found to display the same functional relationship already reported for GX 339−4 between radio and X-ray flux, namely Sradio∝S+0.7X. 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 Lradio∝L+0.7X. Under the hypothesis of common physics driving the disc–jet coupling in different sources, the observed spread to the best-fitting 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 ≲ 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 therefore implying 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 into 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 LX≃ 4 × 10−5LEdd.