Cygnus X-1 is a Galactic black-hole binary and a microquasar. Its X-ray emission originates most likely in the accretion flow, while the radio emission is from a magnetized jet. We study long-term cross-correlations between its X-ray and radio fluxes, searching for lags of the peak of the correlation. We use soft X-ray data from the All Sky Monitor on board of Rossi X-ray Timing Explorer, hard X-ray data from the Burst Alert Telescope on board of Neil Gehrels Swift, and 15 GHz radio monitoring data from the Ryle and AMI telescopes, which light curves cover all of the spectral states of Cyg X-1. Previous studies of radio/X-ray correlations in black-hole binaries concentrated on the soft X-ray/radio correlation in the hard spectral state. In contrast, our strongest correlation is between the hard X-rays and radio in the entire data at a $\lesssim 1$-day lag. This indicates the jet formation from a hard X-ray emitting corona/hot accretion flow through all states of Cyg X-1. We also find evidence for a long lag of the radio with respect to the soft X-rays in the soft state. This indicates long-term advection of the magnetic field through the accretion disc from its high-mass donor, which is similar to the case of another microquasar with a high-mass donor, Cyg X-3.