Cohesin not only links sister chromatids but also inhibits the transcriptional machinery’s interaction with and movement along chromatin^,,,,,. In contrast, replication forks must traverse such cohesin-associated obstructions to duplicate the entire genome in S phase. How this occurs is unknown. Through single-molecule analysis, we demonstrate that the replication factor C (RFC)–CTF18 clamp loader (RFC^CTF18)^, controls the velocity, spacing and restart activity of replication forks in human cells and is required for robust acetylation of cohesin’s SMC3 subunit and sister chromatid cohesion. Unexpectedly, we discovered that cohesin acetylation itself is a central determinant of fork processivity, as slow-moving replication forks were found in cells lacking the Eco1-related acetyltransferases ESCO1 or ESCO2 (refs ) (including those derived from Roberts’ syndrome patients, in whom ESCO2 is biallelically mutated) and in cells expressing a form of SMC3 that cannot be acetylated. This defect was a consequence of cohesin’s hyperstable interaction with two regulatory cofactors, WAPL and PDS5A (refs , ); removal of either cofactor allowed forks to progress rapidly without ESCO1, ESCO2, or RFC^CTF18. Our results show a novel mechanism for clamp-loader-dependent fork progression, mediated by the post-translational modification and structural remodelling of the cohesin ring. Loss of this regulatory mechanism leads to the spontaneous accrual of DNA damage and may contribute to the abnormalities of the Roberts’ syndrome cohesinopathy.