Using complete samples of steep-spectrum quasars, we present evidence for a correlation between radio and optical luminosity which is not caused by selection effects, nor caused by an orientation dependence (such as relativistic beaming), nor a byproduct of cosmic evolution. We argue that this rules out models of jet formation in which there are no parameters in common with the production of the optical continuum. This is arguably the most direct evidence to date for a close link between accretion onto a black hole and the fuelling of relativistic jets. The correlation also provides a natural explanation for the presence of aligned optical/radio structures in only the most radio luminous high-redshift galaxies.